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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?
- a)1545
- b)1626
- c)1722
- d)1768
- e)1844
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
There are 8 men and 7 women. In how many ways a group of 5 people can ...
C) 1722
Explanation: Case 1: 3 men and 2 women 8C3 * 7C2 = 1176
Case 2: 4 men and 1 women 8C4 * 7C1 = 490
Case 3: all 5 men 8C5 = 56
Add all the cases.
Explanation: Case 1: 3 men and 2 women 8C3 * 7C2 = 1176
Case 2: 4 men and 1 women 8C4 * 7C1 = 490
Case 3: all 5 men 8C5 = 56
Add all the cases.
Most Upvoted Answer
There are 8 men and 7 women. In how many ways a group of 5 people can ...
To solve this problem, we need to consider two cases:
Case 1: Exactly 3 men and 2 women are in the group.
The number of ways to select 3 men from 8 is C(8,3) = 56.
The number of ways to select 2 women from 7 is C(7,2) = 21.
The total number of ways to form a group with 3 men and 2 women is 56 x 21 = 1176.
Case 2: 4 men and 1 woman OR 5 men are in the group.
The number of ways to select 4 men from 8 is C(8,4) = 70.
The number of ways to select 1 woman from 7 is C(7,1) = 7.
The total number of ways to form a group with 4 men and 1 woman is 70 x 7 = 490.
The number of ways to select 5 men from 8 is C(8,5) = 56.
The total number of ways to form a group with 5 men is 56.
Therefore, the total number of ways to form a group with at least 3 men is 1176 + 490 + 56 = 1722.
Hence, the correct answer is option C.
Case 1: Exactly 3 men and 2 women are in the group.
The number of ways to select 3 men from 8 is C(8,3) = 56.
The number of ways to select 2 women from 7 is C(7,2) = 21.
The total number of ways to form a group with 3 men and 2 women is 56 x 21 = 1176.
Case 2: 4 men and 1 woman OR 5 men are in the group.
The number of ways to select 4 men from 8 is C(8,4) = 70.
The number of ways to select 1 woman from 7 is C(7,1) = 7.
The total number of ways to form a group with 4 men and 1 woman is 70 x 7 = 490.
The number of ways to select 5 men from 8 is C(8,5) = 56.
The total number of ways to form a group with 5 men is 56.
Therefore, the total number of ways to form a group with at least 3 men is 1176 + 490 + 56 = 1722.
Hence, the correct answer is option C.
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Community Answer
There are 8 men and 7 women. In how many ways a group of 5 people can ...
C) 1722
Explanation: Case 1: 3 men and 2 women 8C3 * 7C2 = 1176
Case 2: 4 men and 1 women 8C4 * 7C1 = 490
Case 3: all 5 men 8C5 = 56
Add all the cases.
Explanation: Case 1: 3 men and 2 women 8C3 * 7C2 = 1176
Case 2: 4 men and 1 women 8C4 * 7C1 = 490
Case 3: all 5 men 8C5 = 56
Add all the cases.
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