Question

At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer in, how many ways can they be allotted to the different wards?

Answer 1

Ward A Ward B Ward C
4 5 8
For ward Awe have to choose 4 out of 20 and then for ward B, 5 out of remaining 16 and then for ward C, 8 out of remaining 11.
${}^{20}{C}_4$ x ${}^{16}{C}_5$ x ${}^{11}{C}_8$
= $\frac{20!}{16!4!}$ x $\frac{16!}{11!5!}$ x $\frac{11!}{8!3!}$ = $\frac{20!}{4!5!3!8!}$
$\frac{20\times 19\times 18\times 17}{24}$ x $\frac{16\times 15\times 14\times 13\times 12}{120}$ x $\frac{11\times 10\times 9}{6}$
= 4845 x 4368 x 165 = 349188400