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Question Number 82111 by john santu last updated on 18/Feb/20
$${a}\:{word}\:{is}\:{formed}\:{with}\:\mathrm{3}\:{vowels} \\ $$$${and}\:\mathrm{3}\:{consonants}\:{without}\: \\ $$$${repetition}\:.\:{the}\:{probability}\:{the} \\ $$$${formation}\:{of}\:{words}\:{begining}\:{the} \\ $$$${letter}\:{z}\:{is}? \\ $$
Commented by john santu last updated on 18/Feb/20
$${i}'\:{got}\:{answer}\:{p}\:=\:\frac{{C}_{\mathrm{2}} ^{\mathrm{20}} }{\mathrm{6}×{C}_{\mathrm{3}} ^{\:\mathrm{21}} } \\ $$$$ \\ $$
Commented by mr W last updated on 18/Feb/20
$${p}=\frac{{C}_{\mathrm{2}} ^{\mathrm{20}} {C}_{\mathrm{3}} ^{\mathrm{5}} \mathrm{5}!}{{C}_{\mathrm{3}} ^{\mathrm{21}} {C}_{\mathrm{3}} ^{\mathrm{5}} \mathrm{6}!}=\frac{{C}_{\mathrm{2}} ^{\mathrm{20}} }{\mathrm{6}{C}_{\mathrm{3}} ^{\mathrm{21}} }=\frac{\mathrm{1}}{\mathrm{42}} \\ $$
Commented by jagoll last updated on 18/Feb/20
$${n}\left({S}\right)\:=\:\mathrm{6}!\:{C}\:_{\mathrm{3}} ^{\mathrm{21}} .{C}_{\mathrm{3}} ^{\mathrm{5}} \\ $$$${n}\left({A}\right)\:=\:\mathrm{5}!\:{C}_{\mathrm{2}} ^{\mathrm{20}} .{C}_{\mathrm{3}} ^{\mathrm{5}} \\ $$$${p}\left({A}\right)\:=\:\frac{\mathrm{5}!\:{C}_{\mathrm{2}} ^{\mathrm{21}} .{C}_{\mathrm{3}} ^{\mathrm{5}} }{\mathrm{6}!\:{C}_{\mathrm{3}} ^{\mathrm{21}} .{C}_{\mathrm{3}} ^{\mathrm{5}} }\:=\:\frac{{C}_{\mathrm{2}} ^{\mathrm{21}} }{\mathrm{6}.{C}_{\mathrm{3}} ^{\mathrm{21}} } \\ $$
Commented by mr W last updated on 18/Feb/20
$$\mathrm{6}\:{is}\:{correct}\:{sir}! \\ $$
Commented by jagoll last updated on 18/Feb/20
$${thank}\:{you}\:{sir} \\ $$$$ \\ $$
Commented by john santu last updated on 18/Feb/20
$${thank}\:{you}.\:{i}\:{wrote}\:{it}\:{wrong}\:\:{because} \\ $$$${in}\:{a}\:{hurry} \\ $$