  # Permutation and Combination - Aptitude Questions and Answers - RejinpaulPlacement 1.
Evaluate: 30 ! / 28 !

Solution:   We have, 30 ! / 28 ! = [30 * 29 * (28 !)] / 28 ! = 30 * 29 = 870 2.
Find the value of
(i) 60 P3
(ii) 4 P4

Solution:   (i) 60 P3 = 60! / (60 - 3) ! = 60 ! /57 !
= [60 * 59 * 58 * (57 !)] / 57 ! = 60 * 59 * 58 = 205320

(ii) 4 P4 = 4! = 4 * 3 * 2 *`1) = 24 3.
Find the value of
(i) 10 C3
(ii) 100 C98
(iii) 50 C50
Answer: d) 120 , 4950 , 1

Solution:   (i) 10 C3 = [10 * 9 * 8] / 3! = [10 * 9 * 8] / [3 * 2 * 1] = 120

(ii) 100 C98 = 100 C(100 - 98) = 100 C2 = [100 * 99] / [2 * 1] = 4950

(iii) 50 C50 = 1 {Since, n Cn = 1} 4.
How many words can be formed by using all letters of the word 'BIHAR'?

Solution:  The word BIHAR contains 5 different letters.

Require num,ber of words = 5 P5 = 5! = (5 * 4 * 3 * 2 * 1) = 120. 5.
How many words can be formed by using all the letters of the word 'DAUGHTER' so that vowels always come together?

Solution:   Give word contaons 8 different letters.

When the vowels AUE are always together, we may suppose them to form an entity, treated as one letter.
Then, the letters to be arranged are DGHTR (AUE).

These 6 letters can be arranged in 6 P6 = 6! = 720 ways.

The vowels in the group (AUE) may be arranged in 3! = 6 ways.

Required number of words = (720 * 6) = 4320 6.
How many words can be formed from the letters of the word 'EXTRA', so that the vowels are never together?

Solution:   The given word contains 5 different letters.

Taking vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).

These letters can be arranged in 4! = 24 ways.

The vowels EA may be arranged amongest themselves in 2! = 2 ways.

Number of words , each having vowels together = (24 * 2) = 48

Total number of words formed by using all the letters of the given words
= 5! = (5 * 4 * 3 * 2 * 1) = 120.

Number of words, each having vowels never together = (120 - 48) = 72. 7.
How many words can be formed from the letters of the word 'DIRECTOR' so that the vowels are always together? 