Question

Find the number of permutations of the letters of the following words
(a) DIVIJA
(b) SARASWATI
(c) REPRESENTATION
(d) COMBINATION

Answer 1

Answer:

(a) 360

(b) 30120

(c) 1816214400

(d) 1663200

Step-by-step explanation:

Hi

(a)

Since there are 6 letters in the word DIVIJA with

I repeating twice,

Since all 6 letters can be arranged in 6! ways, and since

I is repeating twice, permutation between 2 I's will result

in same arrangement , so we need to divide by 2, hence

total number of arrangements are 6!/2! = 360

(b)

Since, there are 9 letters in the word SARASWATI with

S repeating twice, A repeating thrice,

Since all 9 letter can be arranged in 9! ways, and since

S is repeating twice, permutation between 2 S's will result

in same arrangement , so we need to divide by 2, Similarly,

since A is repeating thrice permutation between 2 A's will result

in same arrangement , so we need to divide by 2, hence

total number of arrangements are 9!/3!2! = 30120

(c)

Since there are 14 letters in the word REPRESENTATION with

R repeating twice, E repeating thrice, N repeating twice and

T repeating twice,

total number of arrangements are 14!/3!2!2!2! = 1816214400.

(d)

Since there are 11 letters in the word COMBINATION with

O repeating twice, I repeating twice, N repeating twice ,

total number of arrangement are 11!/3!2!2! = 1663200.

Hope, it helps !

Answer 2

Answer:

Concept: using concept of combination to solve this question

Given: words given

(a) DIVIJA

(b) SARASWATI

(c) REPRESENTATION

(d) COMBINATION

To find: Find the number of permutations of the letters of the  above words given

Step-by-step explanation:

(a)

as we know that there are 6 letters in the word DIVIJA with I which is repeated twice

now,  Since all 6 letters can be arranged in 6! ways, and  I is repeating twice, permutation of  2 I's will result in same arrangement , so we need to divide by 2, hence total number of arrangements are 6!/2! = 360

(b)

as we know that , there are 9 letters in the word SARASWATI with S which is  repeated twice, A repeated thrice, Since all 9 letter can be arranged in 9! ways, and since S is repeating twice, permutation between 2 S's will result in same arrangement , so we need to divide by 2, Similarly, since A is repeating thrice permutation between 2 A's will result in same arrangement , so we need to divide by 2, hence

total number of arrangements are 9!/3!2! = 30120

(c)

as we know that,  there are 14 letters in the word REPRESENTATION with

R which is  repeated twice, E repeating thrice, N repeating twice and

T repeating twice, total number of arrangements are 14!/3!2!2!2! = 1816214400.

(d)

as we know that  there are 11 letters in the word COMBINATION with O which is repeated  twice, I repeating twice, N repeating twice ,

total number of arrangement are 11!/3!2!2! = 1663200.

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