8
Q:

A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?

 A) 210 B) 168 C) 1260 D) 10!/6!

Explanation:

we can select the 5 member team out of the 8 in 8C5 ways = 56 ways.

The captain can be selected from amongst the remaining 3 players in 3 ways.

Therefore, total ways the selection of 5 players and a captain can be made = 56x3 = 168 ways.

(or)

Alternatively, A team of 6 members has to be selected from the 8 players. This can be done in 8C6 or 28 ways.

Now, the captain can be selected from these 6 players in 6 ways.

Therefore, total ways the selection can be made is 28x6 = 168 ways.

Q:

The number of ways in which 8 distinct toys can be distributed among 5 children?

 A) 5P8 B) 5^8 C) 8P5 D) 8^5

Explanation:

As the toys are distinct and not identical,

For each of the 8 toys, we have three choices as to which child will receive the toy. Therefore, there are ${\mathbf{5}}^{\mathbf{8}}$ ways to distribute the toys.

Hence, it is ${\mathbf{5}}^{\mathbf{8}}$ and not ${\mathbf{8}}^{\mathbf{5}}$.

0 185
Q:

In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?

 A) 1440 B) 720 C) 2250 D) 3600

Explanation:

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

0 176
Q:

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

 A) 89,972 B) 90,720 C) 72,000 D) 81,000

Explanation:

The given word HAPPYHOLI has 9 letters

These 9 letters can e arranged in 9! ways.

But here in the given word letters H & P are repeated twice each

Therefore, Number of ways these 9 letters can be arranged is

4 329
Q:

How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets.

 A) 60 B) 120 C) 240 D) 30

Explanation:

Given letters are k, l, m, n, o = 5

number of letters to be in the words = 3

Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters =

5 294
Q:

The letters of the word PROMISE are to be arranged so that three vowels should not come together. Find the number of ways of arrangements?

 A) 4320 B) 4694 C) 4957 D) 4871

Explanation:

Given Word is PROMISE.

Number of letters in the word PROMISE = 7

Number of ways 7 letters can be arranged = 7! ways

Number of Vowels in word PROMISE = 3 (O, I, E)

Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways

Now, the number of ways of arrangements so that three vowels should not come together

= 7! - (5! x 3!) ways = 5040 - 720 = 4320.

7 492
Q:

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

 A) 2520 B) 5040 C) 1260 D) None

Explanation:

The 7 letters word 'POVERTY' be arranged in $\mathbf{7}{\mathbit{P}}_{\mathbf{7}}$ ways = 7! = 5040 ways.

11 416
Q:

A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?

 A) 18 B) 24 C) 36 D) 32

Explanation:

Required Number of ways = = 36

15 484
Q:

How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?

 A) 8640 B) 720 C) 3620 D) 4512

Explanation:

Let the 6 digits of the required 6 digit number be abcdef

Then, the number to be odd number the last digit must be odd digit i.e 3, 5, 7 or 9

The first digit cannot be ‘0’ => possible digits = 3, 5, 7, 2, 6, 8

Remaining 4 places can be of 6 x 5 x 4 x 3 ways

This can be easily understood by

Therefore, required number of ways = 6 x 6 x 5 x 4 x 3 x 4 = 36 x 20 x 12 = 720 x 12

8640 ways.