Question

From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
A.246
B.340
C.290
D.315

Answer 1

A. 246 is the correct answer for this question.

Answer 2

Answer:

The correct answer is $246$.

Step-by-step explanation:

A committee can be formed in the ways given below :

$(1 lady + 4 gents)$ or $(2 ladies + 3 gents)$ or $(3 ladies + 2 gents)$ or $(4 ladies + 1 gents)$ or $(5 ladies + 0 gents)$  

(since at least $1$ lady must be included)

Number of combinations ⁿC$_{r}$ $= \frac{n!}{((n - r)! r!)}$

Here, total number of combinations :

(⁴C₁ ₓ ⁶C₄) $+$ (⁴C₂ ₓ ⁶C₃) $+$ (⁴C₃ ₓ ⁶C₂) $+$ (⁴C₄ ₓ ⁶C₁)

$=60 +120 +60 +6 \\= 246$

Therefore the total number of possible combinations for including at least a lady in the committee is $246$.