Question

A school wants to celebrate an annual function in their school and a teacher has been given responsibility to organize the function. The teacher wants to form a committee of 5 students from a group of students consisting 4 girls and 7 boys to
organize the annual function.
(1)How many ways the committee can be formed with no girl.
a)21
6441
c)91
d)301
(ii) How many ways the committee can be formed with at least one boy and one girl
a)21
b)441
c)91
d)301
(iii) How many ways the committee can be formed with at least 3 girls ?
a)21
b)441
c)91
d)301
(IV) How many ways the committee can be formed with at least 2 girls ?
a)21
b)441
c)91
d)301
(V) How many ways the committee of 7 can be formed with exactly 3 girls if the committee consists of 2 more boys ?

Answer 1

Answer:

part 1 : a)

part 2 : b)

part 3 : c)

part 4 : d)

part 5 : 140

Step-by-step explanation:

Here combination will be used. (nCr)

where n is the total available and r is the no that should be taken out of n.

PART 1

Committe with no girl : 7C5 = 7! / (7-5)!* 2! = 21

PART 2

atleast 1 B and 1 G, there will be 4 cases.

1 B 4G : 7C1 * 4C4 = 7

2B 3G : 7C2 * 4C3 = 84

3B 2G : 7C3 * 4C2 = 210

4B 1G : 7C4 * 4C1 = 140

TOTAL = 7+84+210+140 = 441

PART 3

atleast 3 G, there will be 2 cases only as the no of girls is 4.

3G 2B : 4C3 * 7C2 = 84

4G 1B : 4C4 * 7C1 = 7

TOTAL = 84 + 7 = 91

PART 4

atleast 2 girls.

2G 3B : 4C2 * 7C3 = 210

3G 2B : 4C3 * 7C2 = 84

4G 1B : 4C4 * 7C1 = 7

TOTAL = 210+84+7 = 301

PART 5

COMMITTEE OF 7.

EXACTLY 3G

4C3 * 7C4 = 4*35 = 140