Permutation & Combination — Page 1

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Question 228798

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Question 228455

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An insect moves from (0,0) to (6,3) by moving through lattice points ((x,y) integers) moving either one unit right or one unit up at each step. Let N be the number of paths in which the line segments joining (2,1),(2,2),(3,2) and (4,2) are avoided. find N.

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there are 32 students in a class. for each competition in a sport event in the school each class can send a team with three students. if no two students may be in the same team for more than one time, in how many different competitions can this class participate?

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There are cards in 30 different colors, with 70 cards of each color. Initially, 70 cards are selected and laid out in a stack from top to bottom. One operation consists of: choosing an X from the bottom 20 cards, such that its color has not appeared in the top 50 cards; then choosing a Y from the top 50 cards, such that its color has appeared at least twice in the top 50 cards; removing X and placing it right above Y. Repeat this process until no more valid X can be chosen. (1) Prove that the number of operations is finite. (2) For all possible initial configurations and sequences of operations, find the maximum possible number of operations.

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Question #227151

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(m/n)

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Question #227098

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Question 226289

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Question 226044

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Question 224709

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Question 224641

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Question #224634

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Question #224623

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Question 224398

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If I have 10 people and I want to create pairings, so that every person is matched with every other person at least once, how many unique pairings will there be in total?

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there are 32 students in a class. for each competition in a sport event in the school each class can send a team with three students. if no two students may be in the same team for more than one time, in how many different competitions can this class participate?

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Question 222105

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Question 221661

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Question 220878

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Question 220877

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Question 220876

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Question 220874

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Question 220873

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Question 220872

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Question 220744

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Question 220743

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Question 220741

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Question 220740

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Question 220739

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Prove that:∀n∈IN ∫^( n+1) _( n) ln(t)dt≤ln(n+(1/2))

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Question 219527

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10 couples are invited to a dinner. after the dinner they form pairs to dance. in how many ways can they do this, 1) generally 2) a man should dance with a woman 3) as 2), but two special couples should not dance with each other 4) a man should dance with a woman, but not with his own wife 5) as 4), but two special couples should not dance with each other

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there are 100 students in a school. it is found out that each student should select at least 4 courses, so that no two students have the same selection. how many different courses does the school offer?

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10 couples are invited to a dinner and should be seated at a round table. in how many ways can the host do this, 1) generally. 2) if the husband and the wife of each couple should sit together. 3) if no two men should sit next to each other. 4) as 3), but two speicial couples should not sit next to each other. it means that the husband from couple 1 may not sit next to the wife from couple 2 and the husband from couple 2 may not sit next to the wife from couple 1. but certainly the husbands of both couples may sit next to their own wifes.

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P(5,6)=((15!)/((15−6))) = ((15!)/(9!)) =((15×14×131×2×11×10×9×8×7×6×5×4×3×2×1)/(9×8×7×6×5×4×3×2×)) =15×14×13×12×11×10 =3,603,600

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how many different words can be formed from the word MATHEMATICS? note: here a word should have at least two letters, but mustn′t have a meaning.

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Question 217402

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Question 214923

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Question 213796

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in how many ways can a teacher divide his 10 studens into 4 groups such that each group has at least 2 students?

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Question 210290

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Find the value of r, if ^(10) C_r = ^(10) C_(2r + 1)

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(( ((n),(0) ) +3 ((n),(1) ) +5 ((n),(2) ) +...+(2n+1) ((n),(n) ))/( ((n),(1) ) +2 ((n),(2) ) + 3 ((n),(3) ) +...+n ((n),(n) ))) =((23)/(11)) n=?

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Question 208263

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Show that (π/4) < ∫_0 ^1 (√(1−x^4 ))dx using x = sint show that ∫_0 ^1 (√(1−x^4 ))dx<((2(√2))/3) using (∫_0 ^1 f(x)g(x)dx)^2 <∫_0 ^1 (f(x))^2 dx∫_0 ^1 (g(x))^2 dx

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An ordered data consists of 6 even numbers and 4 odd numbers. The average of the odd numbers is 2022. The 3rd, 5th, 6th and 8 th numbers are odd. The data range is 24 , and the interquartile range is 14. The largest possible average of the ten numbers is ___