Question

9 students of class 12th of whom 2 from section A, 3
from section B and 4 from section C are available for
inter school debate competition. Number of ways in
which 4 students can be selected so that there is atleast
1 from each section, is
(A) 144
(B) 120
(C)72
(D)71​

Answer 1

Answer:

I think the answer is option a

Answer 2

Given that,

Number of total students = 9

From section A = 2

From section B= 3

From section C = 4

For  inter school debate competition,

Number of ways in  which 4 students can be selected so that there is at least  1 from each section,

For first case,

2 students from section A, 1 students from section B and 1  students from section C

For second case,

1 students from section A, 2 students from section B and 1  students from section C

For third case,

1 students from section A, 1 students from section B and 2  students from section C

We need to calculate the number of ways

Using all combination

$Number\ of\ ways=^{2}C_{2}\times^3C_{1}\times^4C_{1}+^2C_1\times^3C_2\times^4C_1+^2C_1\times^3C_1\times^4C_2$

$Number\ of\ ways=1\times3\times4+2\times3\times4+2\times3\times6$

$Number\ of\ ways=12+24+36$

$Number\ of\ ways=72$

Hence, The number of ways are 72.

(C) is correct option.