Question

Each of the $3$ committees has $1$ vacancy can be filled from a group of $6$ people. Find the number of ways the $3$ vacancies can be filled if:
(i) Each person can serve on almost $1$ committee.

Answer 1

Select on commitee out of $3={3_C}_1$

Select one person out of $6={6_C}_1$

Select on commitee out of $2={2_C}_1$

Select one person out of $5={5_C}_1$

Select last commitee$=1$

Select one person out of $4={4_C}_1$

number of ways the $3$ vacancies can be filled if Each person can serve on atmost $1$ committee$={6_C}_1\times {2_C}_1\times 1\times {4_C}_1$

$=6\times 2\times 1\times 4=48$ways