Question

Suppose there are 14 men and 16 women in a cooking club, and you would like to choose a team to represent the USC Cooking Club in the National Culinary Arts Competition a) How many possible groups can you choose if you need a team of 4 members? b) How many possible groups can you choose if the team needs 3 members: a captain, a vice-captain and a regular member? c) How many possible groups can you choose if the team needs 4 members: a captain, 2 vice-captains, and a regular member? d) How many possible groups can you choose if you need a Men's team and a Women's team consisting of 3 members cach?

Answer 1

Answer:

Step-by-step explanation:

No of men =14 :  

No of women = 16

a) 4 members can be selected in 30C4 ways = 27405 ways

b) If one captain, one vice captain and one regular member.

We have 30 choices for captain, 29 for vice captain and 28 for regular member

no of groups$= 30(29)(28)=24360$

c) For one captain, 2 vice captains and one regular member

no of groups = $30C1*29C2*28C1 \\=341040$

d) Men's team 3 members  can be selected in 14C3 ways

and women team 3 members can be selected in 17C3 ways

No of groups =$14C3*17C3 =247520$