JAMB Mathematics Past Questions & Answers - Page 388

1,938.

A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly

A.

378 ways

B.

462 ways

C.

840 ways

D.

924 ways

Correct answer is A

\(^{3}C_{1} \times ^{9}C_{5}=\frac{3!}{(3-1)!1!}\times \frac{9!}{(9-5)!5!}\\=\frac{3!}{2!1!}\times \frac{9!}{4!5!}\\=\frac{3 \times 2!}{2!\times 1}\times \frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}\\=3\times9\times2\times7\\=378 \hspace{1mm}ways\)

1,939.

A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medals is selected at the random from the container, what is the probability that it is not a gold medal?

A.

9/35

B.

11/35

C.

4/7

D.

3/7

Correct answer is C

Gold medals = 30
silver medals = 22
Bronze medals = 18/70
P(Gold medals) = 30/70 = 3/7
∴ P(not Gold medal) = 1 - 3/7
= 4/7

1,940.

The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group

A.

9

B.

7

C.

42

D.

15

Correct answer is A

Let the number of students = x
Total age of the students = 15x
Total age including age of the teacher = 15x + 45
Mean of their ages; (15x + 45)/(x + 1) = 18
15x + 45 = 18(x + 1)
15x + 45 = 18x + 18
18x - 15x = 45 - 18
3x = 27
x = 9