In how many ways can the letters of the word “CORPORATION” be arranged so that vowels always come together.

5760

50400

2880

None of above

Answer And Explanation

Answer: Option B

Explanation:

Vowels in the word “CORPORATION” are O,O,A,I,O

Lets make it as CRPRTN(OOAIO)

This has 7 lettes, where R is twice so value = 7!/2!

= 2520

Vowel O is 3 times, so vowels can be arranged = 5!/3!

= 20

Total number of words = 2520 * 20 = 50400

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there

109

128

138

209

Answer And Explanation

Answer: Option D

Explanation:

In a group of 6 boys and 4 girls, four children are to be selected such that

at least one boy should be there.

So we can have

(four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils)

This combination question can be solved as

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done

456

556

656

756

Answer And Explanation

Answer: Option D

Explanation:

From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.

So we can have

(5 men) or (4 men and 1 woman) or (3 men and 2 woman)

A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw

64

128

132

222

Answer And Explanation

Answer: Option A

Explanation:

From 2 white balls, 3 black balls and 4 red balls, 3 balls are to be selected such that

at least one black ball should be there.

Hence we have 3 choices

All three are black

Two are black and one is non black

One is black and two are non black

Total number of ways

= 3C3 + (3C2 x 6C1) + (3C1 x 6C2) [because 6 are non black]

=1+[3×6]+[3×((6×5)/(2×1))]=1+18+45=64

Ques. A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours

12

24

48

168

Answer And Explanation

Answer: Option B

Explanation:

This question seems to be a bit typical, isn’t, but it is simplest.

1 red ball can be selected in 4C1 ways

1 white ball can be selected in 3C1 ways

1 blue ball can be selected in 2C1 ways

Total number of ways

= 4C1 x 3C1 x 2C1

= 4 x 3 x 2

= 24

Please note that we have multiplied the combination results, we use to add when their is OR condition, and we use to multiply when there is AND condition, In this question it is AND as

1 red AND 1 White AND 1 Blue, so we multiplied.

Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

1/3

1/6

1/2

1/8

Answer And Explanation

Answer: Option C

Explanation:

Total cases are = 2*2*2 = 8, which are as follows

[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]

Favoured cases are = [TTH, THT, HTT, TTT] = 4

So required probability = 4/8 = ½

Ques. In a throw of dice what is the probability of getting number greater than 5

1/2

1/3

1/5

1/6

Answer And Explanation

Answer: Option D

Explanation:

Number greater than 5 is 6, so only 1 number

Total cases of dice = [1,2,3,4,5,6]

So probability = ⅙