Ben needs to form a committee of 3 from a group of 8 engineers to study design improvements for a product. If two of the engineers are too inexperienced to serve together on the committee, how many different committees can Ben form?
A. 20
B. 30
C. 50
D. 56
E. 336

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A) 5 to 4
B) 3 to 2
C) 2 to 1
D) 5 to 1
E) 6 to 1

There are seven empty seat on a bus and four people entre . In how many ways can be seated ?

A) 3024
B) 840
C) 720
D) 120
E) 24

Out of 18 points in a plane ,no three are in same straight line except five points which are collinear. The number of triangles, which can be formed by joining them is

A) 816
B) 806
C) 800
D) 750
E) 676

From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?

A. 1/10

B. 4/9

C. 1/2

D. 3/5

E. 2/3

How many ways to choose a committee of 3 people from 4 couples so that no couple is chosen.

A) 36
B) 48
C) 210
D) 306
E) None of these

In a certain group of 10 members, 4 members teach only French and the rest teach only German or Spanish. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committee can be chosen?

a) 40
b) 50
c) 64
d) 80
e) 100

Please suggest how to solve the problem. The OA is e.

The number of ways in which three letters be posted in four letter boxes in a village, if all the three letters are not posted in the same letter box.

A) 64
B) 60
C) 81
D) 78
E) None of these