Question

There are 8 men and 7 women .in how many ways a group of 5 people can be made such that at least 3 men are there in the group

Answer 1

in 3 groups 2women and 3 men and in other two also the same

Answer 2

Answer:

1722 ways

Step-by-step explanation:

Number of men = 8

Number of women = 7

Now we are supposed to find no. of ways a group of 5 people can be made such that at least 3 men are there in the group

For group of 5 with atleast 3 men

Case 1: 3 men and 2 women

No. of ways = $^8C_3 \times ^7C_2=\frac{8!}{3!(8-3)!} \times \frac{7!}{2!(7-2)!}=1176$

Case 1: 4 men and 1 women

No. of ways = $^8C_4 \times ^7C_1=\frac{8!}{4!(8-4)!} \times \frac{7!}{1!(7-1)!}=490$

Case 1: 5 men

No. of ways = $^8C_5=\frac{8!}{5!(8-5)!}=56$

So, Total no. of ways of making a group of 5 people can be made such that at least 3 men = 1176+490+56=1722

Hence There are 1722 ways