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

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Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1 percent grade, y gallons of 2 percent grade and z gallons of 3 percent grade are mixed to give x+y+z gallons of 1.5 percent grade, what is x in terms of y and z?

A. y + 3z
B. (y+z)/4
C. 2y + 3z
D. 3y + z
E. 3y + 4.5z

There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

(A) 20

(B) 25

(C) 40

(D) 60

(E) 125

In an examination there are three multiple choice questions and each questions has 4 choices. Number of sequences in which students can fail to get all answers correct ?

A) 11
B) 15
C) 63
D) 80
E) 83

The number of different arrangements that can be made with the letters of the word ”GRATITUDE” in which the T’s are together?

A) 9!*2!
B) 8!
C) 9!
D) 81*2!
E) None of these

A vessel is filled with a liquid in which 5 parts are milk and 3 parts are water. What fraction of mixture must be drawn off are replaced with water. So that the mixture may be half water and half milk.

a) 1/2
b) 1/3
c) 2/3
d) 1/5
e) 1/8

At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total nummber of different possible seating arrangements for the group?

(A) 5
(B) 10
(C) 24
(D) 32
(E) 120

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

Jake, Lena, Fred, John and Inna need to drive home from a party in a car that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?

a. 30
b. 42
c. 60
d. 120
e. 125

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