Aptitude  Permutations  Practice Q&A

Answer: 36
Explanation:

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = ³P₃ = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = ³P₃ = 3! = 6.

Total number of ways = $\left(6 \times 6\right)$ = 36.

Answer: 64
Explanation:

We may have[1 black and 2 non-black] or [2 black and 1 non-black] or [3 black].

Answer: 20
Explanation:

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

$\therefore$ Required number of numbers = $\left(1 \times 5 \times 4\right)$ = 20.

Answer: 25200
Explanation:

Number of ways of selecting [3 consonants out of 7] and [2 vowels out of 4]

Number of groups, each having 3 consonants and 2 vowels = 210.

Each group contains 5 letters.

$\therefore$ Required number of ways = $\left(210 \times 120\right)$ = 25200.

Answer: 360
Explanation:

The word LEADER contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

Answer: 1680
Explanation:

The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.

Given that no digit appears more than once. Hence we have 8 digits remaining (0,1,2,4,6,7,8,9)

So, the next 4 places can be filled with the remaining 8 digits in ⁸P₄ ways.

Total number of ways = ⁸P₄=8×7×6×5=1680

Answer: 720
Explanation:

The word LEADING has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG [EAI].

Now, 5 [4 + 1 = 5] letters can be arranged in 5! = 120 ways.

The vowels [EAI] can be arranged among themselves in 3! = 6 ways.

$\therefore$ Required number of ways = $\left(120 \times 6\right)$ = 720.

Answer: 80
Explanation:

He has 10 patterns of chairs and 8 patterns of tables

A chair can be selected in 10 ways.

A table can be selected in 8 ways.

Hence one chair and one table can be selected in 10×80 ways =80ways

Answer: 2880
Explanation:

Around a circle, 5 boys can be arranged in 4! ways.

Given that the boys and the girls alternate. Hence there are 5 places for the girls. Therefore the girls can be arranged in 5! ways.

Total number of ways

Answer: 120
Explanation:

The word BIHAR has 5 letters and all these 5 letters are different.

Total number of words that can be formed by using all these 5 letters

= ⁵P₅=5

=5×4×3×2×1=120