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The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies is
  • a)
    252
  • b)
    672
  • c)
    444
  • d)
    420
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The number of ways in which a committee of 6 members can be formed fro...
A committee of 6 members is to formed from 8 gentlemen and 4 ladies by taking
(i) 3 lady out of 4 and 3 gentlemen out of 8
(ii) 4 lady out of 4 and 2 gentlemen out of 8
In case (i) the number of ways = 4c3 x 8c3
= 4 x 56 = 224
In case (ii) the number of ways = 4c4 x 8c2
= 1 x 28 = 28
Hence, the required number of ways = 224 + 28 = 252
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Most Upvoted Answer
The number of ways in which a committee of 6 members can be formed fro...
To solve this problem, we can use the concept of combinations.

Step 1: Determine the number of ways to select exactly 3 ladies and 3 gentlemen for the committee.
We can choose 3 ladies out of 4 in C(4, 3) ways, which is equal to 4.
Similarly, we can choose 3 gentlemen out of 8 in C(8, 3) ways, which is equal to 56.
Therefore, the number of ways to select exactly 3 ladies and 3 gentlemen is 4 * 56 = 224.

Step 2: Determine the number of ways to select exactly 4 ladies and 2 gentlemen for the committee.
We can choose 4 ladies out of 4 in C(4, 4) ways, which is equal to 1.
Similarly, we can choose 2 gentlemen out of 8 in C(8, 2) ways, which is equal to 28.
Therefore, the number of ways to select exactly 4 ladies and 2 gentlemen is 1 * 28 = 28.

Step 3: Determine the number of ways to select exactly 5 ladies and 1 gentleman for the committee.
We can choose 5 ladies out of 4, which is not possible, so the number of ways is 0.

Step 4: Determine the number of ways to select all 6 ladies for the committee.
We can choose all 6 ladies out of 4, which is not possible, so the number of ways is 0.

Step 5: Determine the number of ways to select at least 3 ladies for the committee.
Now, we add up the results from steps 1, 2, 3, and 4.
224 + 28 + 0 + 0 = 252.

Therefore, the number of ways to form a committee of 6 members that contains at least 3 ladies is 252.
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In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girlsG1, G2, G3, G4, G5.(i) Let α1 be the total number of ways in which the committee can be formed such that the committee has5 members, having exactly 3 boys and 2 girls.(ii) Let α2 be the total number of ways in which the committee can be formed such that the committee hasat least 2 members, and having an equal number of boys and girls.(iii) Let α3be the total number of ways in which the committee can be formed such that the committee has5 members, at least 2 of them being girls.(iv) Let α4be the total number of ways in which the committee can be formed such that the committee has4 members, having atleast 2 girls and such that both M1 and G1 are NOT in the committee together.The correct option is

In a high school, a committee has to be formed from a group of 6 boys M1, M2,M3, M4,M5, M6 and 5 girls G1,G2, G3, G4, G5.(i) Let α1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.(ii) Let α2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.(iii) Let α3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.(iv) Let α4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M1 and G1 are NOT in the committee together.The correct option is

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The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies isa)252b)672c)444d)420Correct answer is option 'A'. Can you explain this answer?
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