A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is

Question

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is (A) 40 (B) 41 (C) 16 (D) 32

Tardigrade Admin · Accepted Answer

Total number of ways =( 2 C 2 × 2 C 2 × 4 C 0)+2( 2 C 1 × 2 C 2 × 4 C 1)+( 2 C 1 × 2 C 1 × 4 C 2) = 1 + 2(8) + 24 = 41

Q. A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is

40

41

16

32

Total number of ways $= (^{2} C_{2} \times^{2} C_{2} \times^{4} C_{0}) + 2 (^{2} C_{1} \times^{2} C_{2} \times^{4} C_{1}) + (^{2} C_{1} \times^{2} C_{1} \times^{4} C_{2})$
$= 1 + 2 (8) + 24 = 41$

Q. A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes atleast 1 lady, atleast 1 old man and atmost 2 young men. Then the total number of ways in which this committee can be formed is

40

41

16

32

Total number of ways =(2C2​×2C2​×4C0​)+2(2C1​×2C2​×4C1​)+(2C1​×2C1​×4C2​) =1+2(8)+24=41

Total number of ways $= (^{2} C_{2} \times^{2} C_{2} \times^{4} C_{0}) + 2 (^{2} C_{1} \times^{2} C_{2} \times^{4} C_{1}) + (^{2} C_{1} \times^{2} C_{1} \times^{4} C_{2})$
$= 1 + 2 (8) + 24 = 41$