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From a group of 6 men and 4 women a committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 2 men?
- a)210
- b)225
- c)195
- d)185
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
From a group of 6 men and 4 women a committee of 4 persons is to be fo...
A committee of 4 Person is to be formed, when the committee has at least 2 men
= (6 C2 x 4 C2) + (6 C3 x 4 C1) + (6 C4 x 4 C0)
= 15 x 6 + 20 x 4 + 15 x 1
= 90 + 80 + 15 = 185
= (6 C2 x 4 C2) + (6 C3 x 4 C1) + (6 C4 x 4 C0)
= 15 x 6 + 20 x 4 + 15 x 1
= 90 + 80 + 15 = 185
Most Upvoted Answer
From a group of 6 men and 4 women a committee of 4 persons is to be fo...
Given: A group of 6 men and 4 women, and a committee of 4 persons is to be formed with at least 2 men.
To find: The number of ways in which the committee can be formed.
Approach:
We can use the combination formula to find the number of ways to form a committee of 4 persons from a group of 10 persons.
We need to subtract the number of committees with 0 or 1 men from the total number of committees to get the committees with at least 2 men.
Total number of ways to form a committee of 4 persons from a group of 10 persons = 10C4
Number of committees with 0 or 1 man = (4C4 * 6C0) + (4C3 * 6C1)
Number of committees with at least 2 men = Total number of committees - Number of committees with 0 or 1 man
Solution:
Total number of ways to form a committee of 4 persons from a group of 10 persons = 10C4
= (10!)/((4!)(10-4)!)
= (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1)
= 210
Number of committees with 0 or 1 man = (4C4 * 6C0) + (4C3 * 6C1)
= (1 x 1) + (4 x 6)
= 25
Number of committees with at least 2 men = Total number of committees - Number of committees with 0 or 1 man
= 210 - 25
= 185
Therefore, the number of different ways in which the committee can be formed so that the committee has at least 2 men is 185. Hence, option (D) is the correct answer.
To find: The number of ways in which the committee can be formed.
Approach:
We can use the combination formula to find the number of ways to form a committee of 4 persons from a group of 10 persons.
We need to subtract the number of committees with 0 or 1 men from the total number of committees to get the committees with at least 2 men.
Total number of ways to form a committee of 4 persons from a group of 10 persons = 10C4
Number of committees with 0 or 1 man = (4C4 * 6C0) + (4C3 * 6C1)
Number of committees with at least 2 men = Total number of committees - Number of committees with 0 or 1 man
Solution:
Total number of ways to form a committee of 4 persons from a group of 10 persons = 10C4
= (10!)/((4!)(10-4)!)
= (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1)
= 210
Number of committees with 0 or 1 man = (4C4 * 6C0) + (4C3 * 6C1)
= (1 x 1) + (4 x 6)
= 25
Number of committees with at least 2 men = Total number of committees - Number of committees with 0 or 1 man
= 210 - 25
= 185
Therefore, the number of different ways in which the committee can be formed so that the committee has at least 2 men is 185. Hence, option (D) is the correct answer.
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From a group of 6 men and 4 women a committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 2 men?a)210b)225c)195d)185Correct answer is option 'D'. Can you explain this answer?
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