Question

q31) Out of 4 gents and 6 ladies,a committee is to be formed find the number of ways the committee can be formed such that it comprises of at least 2 gents and at least the number of ladies should be double of gents. (a) 94, (b) 132 (c) 136, (d) 104​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

136 would be the number of ways the committee can be formed with at least 2 gents and the ladies must be at least double of gents.

Step-by-step explanation:

Given that,

Number of gents = 4

Number of ladies = 6

Now, the committee formed must include a minimum of two men and the ladies must be at least double of gents

So,

The possible combinations can be;

2gents - 4 ladies    $^{4} C_{2}$ * $^{6} C_{4}$

2 gents - 5 ladies    $^{4} C_{2} * ^{6} C_{5}$

2 gents - 6 ladies    $^{4} C_{2} * ^{6} C_{6}$

3 gents - 6 ladies  $^{4} C_{3} * ^{6} C_{6}$

By solving,

$^{4} C_{2}$ * $^{6} C_{4}$ + $^{4} C_{2} * ^{6} C_{5}$ + $^{4} C_{2} * ^{6} C_{6}$ +  $^{4} C_{3} * ^{6} C_{6}$

6 * (6 *5)/2 + 6 * 6 + 6* 1 + 4 * 1

= 90 + 36 + 6 + 4

= 136

Thus, in 136 ways the committee can be formed with at least 2 gents and the ladies must be at least double of gents. Hence, option C is the correct answer.

Learn more: Permutation and Combination

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