JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Permutations and Combinations

There are ten boys

B_{1}, B_{2}, \dots, B_{10}

and five girls

G_{1}, G_{2}, \dots, G_{5}

in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both

B_{1}

and

B_{2}

together should not be the members of a group, is ______.

Answer: 1120

Solution

Total ways to select 3 boys from 10 and 3 girls from 5:

^{10} C_{3} \times^{5} C_{3} = \frac{10 \times 9 \times 8}{6} \times \frac{5 \times 4}{2} = 120 \times 10 = 1200

Ways when both

B_{1}

and

B_{2}

are together (need 1 more boy from remaining 8):

^{8} C_{1} \times^{5} C_{3} = 8 \times 10 = 80

Ways when

B_{1}

and

B_{2}

are NOT together:

1200 - 80 = 1120

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Integer answer