15
Q:

# Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.

 A) 28 B) 14 C) 21 D) 7

Explanation:

Let x, y, z be the number of balls received by the three persons, then

Let

$∴$ x + y + z =21

$⇒$ u + 5 + v + 5 + w + 5 = 21

$⇒$ u + v + w = 6

$∴$Total number of solutions = $C3-16+3-1=C28=28$

Q:

There are 5 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next two have 6 choices each?

 A) 1112 B) 2304 C) 1224 D) 2426

Explanation:

Number of questions = 5
Possibilities of choices for each question 1 to 5 respectively = 4, 4, 4, 6, 6

Reuired total number of sequences

= 4 x 4 x 4 x 6 x 6

= 2304.

5 143
Q:

How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?

 A) 120 B) 240 C) 256 D) 360

Explanation:

Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are

5 x 4 x 3 x 2 x 1 = 120.

3 176
Q:

What is the value of ?

 A) 10000 B) 9900 C) 8900 D) 7900

Explanation:

Here in 100P2, P says that permutations and is defined as in how many ways 2 objects can be selected from 100 and can be arranged.

That can be done as,

= 100!/(100 - 2)!

= 100 x 99 x 98!/98!

= 100 x 99

= 9900.

1 719
Q:

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels always come together?

 A) 720 B) 1440 C) 1800 D) 3600

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

Number of vowels in the given word = 2 = A & E

Required number of different ways, the letters of the word THERAPY arranged such that vowels always come together is

6! x 2! = 720 x 2 = 1440.

6 472
Q:

In how many different ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together?

 A) 112420 B) 85120 C) 40320 D) 1209600

Explanation:

Given word is TRANSFORMER.

Number of letters in the given word = 11 (3 R's)

Required, number of ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together is

10! x 2!/3!

= 3628800 x 2/6

= 1209600

3 485
Q:

In how many ways the letters of the word 'CIRCUMSTANCES' can be arranged such that all vowels came at odd places and N always comes at end?

 A) 1,51,200 ways. B) 5,04,020 ways C) 72,000 ways D) None of the above

Explanation:

In circumcstances word there are 3C's, 2S's, I, U,R, T, A, N, E

Total = 13 letters

But last letter must be N

Hence, available places = 12

In that odd places = 1, 3, 5, 7, 9, 11

Owvels = 4

This can be done in 6P4 ways

Remaining 7 letters can be arranged in 7!/3! x 2! ways

Hence, total number of ways = 6P4 x 7!/3! x 2! = 360 x 5040/12 = 1,51,200 ways.

2 606
Q:

In how many different ways can the letters of the word 'RITUAL' be arranged?

 A) 720 B) 5040 C) 360 D) 180

Explanation:

The number of letters in the given word RITUAL = 6

Then,

Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!

=> 6 x 5 x 4 x 3 x 2 x 1 = 720

3 559
Q:

How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.

 A) 64 B) 63 C) 62 D) 60

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.