a team of 5 members is to be chosen from 7 men and 8 women it is decided that there can be at most 3 men in the team how many different ways are there to choose team
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Given , Total number of members to selected in a team = 5
Number of men = 7 and the number of women = 8
It is given that the team can have atmost 3 men.
There are many cases in which the team can be formed.
Case 1 -
3 Men , 2 women
No. Of ways = 7C3 × 8C2 = 980
Case 2 -
2 Men , 3 Women
No. Of ways = 7C2 × 8C3 = 1176
Case 3 -
1 Man , 4 women
No. Of ways = 7C1 × 8C4 = 490
Case 4 -
5 Women
No. Of ways = 8C5 = 56
Total number of ways in which the team can be formed = 980 + 1176 + 490 + 56 = 2702
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