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Q:

In how many different ways can five persons stand in a line for a group photograph?

A) 120	B) 240
C) 360	D) 720

Answer & Explanation Answer: A) 120

Explanation:

This is the number of permutations of five things taken all at a time.

Therefore, answer = $5 P_{5}$ = 120 ways

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Q:

How many 3 letters words can be formed using the letters of the words hexagon?

A) 120	B) 210
C) 160	D) 200

Answer & Explanation Answer: B) 210

Explanation:

Since the word hexagon contains 7 different letters,the number of permutations is $7 P_{3}$ = 7 x 6 x 5 =210

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Q:

The diagonal of the floor of a rectangular closet is 7 $\frac{1}{2}$ feet. The shorter side of the closet is 4 $\frac{1}{2}$ feet. What is the area of the closet in square feet?

A) 9	B) 18
C) 27	D) 36

Answer & Explanation Answer: C) 27

Explanation:

Other side = $\sqrt{d^{2} - s^{2}}$ = $\sqrt{(\frac{225}{4} - \frac{81}{4})}$ = $\sqrt{\frac{144}{4}}$ = 6 ft

Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

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Q:

In how many ways can you choose one or more of 12 different candies?

A) 4054	B) 4050
C) 4095	D) 4059

Answer & Explanation Answer: C) 4095

Explanation:

Each candy can be dealt with in two ways.It can be chosen or not chosen.This will give 2 possibilites for the first candy, 2 for the second, and so on.by multiplying the cases together we get $2^{12}$ . Since the case of no candy being selected is not an option, we have to subtract 1 from our answer.

Therefore,there are $2^{12}$ - 1 = 4095 ways of selecting one or more candies

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Q:

If there are 15 dots on a circle,how many triangles can be formed?

A) 455	B) 450
C) 469	D) 500

Answer & Explanation Answer: A) 455

Explanation:

There are 15 dots in total,and to make a triangle we need to select any three of those dots.

So, $15 C_{3}$ = 455

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Q:

If each of the 8 teams in a league must play each other three times,how many games will be played?

A) 72	B) 84
C) 36	D) 79

Answer & Explanation Answer: B) 84

Explanation:

Since,each member of the league must meet every other member of the league.If they only played each other once,there would be $8 C_{2}$ games.Since,each pairing of teams will occur three times,the answer will be triple.

Therfore, $8 C_{2} * 3$ =84

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Q:

A polygon 7 sides.How many diagonals can be formed?

A) 14	B) 7
C) 15	D) 21

Answer & Explanation Answer: A) 14

Explanation:

$7 C_{2}$ - 7 = 14

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Q:

12 people at a party shake hands once with everyone else in the room.How many handshakes took place?

A) 72	B) 66
C) 76	D) 64

Answer & Explanation Answer: B) 66

Explanation:

There are 12 people, so this is our n value.

So, $12 C_{2}$ 1= 66

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