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
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?
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.
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
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 ___