A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

Question

A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees? (A) 320 (B) 160 (C) 80 (D) 200

Tardigrade Admin · Accepted Answer

Out of 5 girls, he has to invite exactly three. This can be done in 5 C 3 ways. Out of the 4 boys, he may invite either one or two or three or four or even none of them. This may be done in (2)4 ways. Thus the total number of ways is 5 C 3 ×(2)4=10 × 16=160

Q. A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

320

160

80

200

Out of 5 girls, he has to invite exactly three. This can be done in $^{5} C_{3}$ ways. Out of the 4 boys, he may invite either one or two or three or four or even none of them. This may be done in $(2)^{4}$ ways. Thus the total number of ways is $^{5} C_{3} \times (2)^{4} = 10 \times 16 = 160$

Q. A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

320

160

80

200

Out of 5 girls, he has to invite exactly three. This can be done in 5C3​ ways. Out of the 4 boys, he may invite either one or two or three or four or even none of them. This may be done in (2)4 ways. Thus the total number of ways is 5C3​×(2)4=10×16=160

Out of 5 girls, he has to invite exactly three. This can be done in $^{5} C_{3}$ ways. Out of the 4 boys, he may invite either one or two or three or four or even none of them. This may be done in $(2)^{4}$ ways. Thus the total number of ways is $^{5} C_{3} \times (2)^{4} = 10 \times 16 = 160$