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4 Word Rearrangement Questions

Below are 4 word rearrangement questions. You have to find the number of different ways letters of words can be changed positions to form new words.

Question 1

Find the number of different ways in which word OPTIMIZE can be rearranged ?

a) 20155 b) 20160 c) 20165 d) 201660

Answer : d) 201660

Number of rearrangements = n! / (r1! x r2!...)

In the above formula, n represents the number of letters in the given word. r1, r2, r3 represent number of repeated words.

In OPTIMIZE there are 8 words. Word I is repeated twice.

Therefore, number of rearrangements = 8!/2! = 20160

Question 2

Find the total number of words that can be formed out of INDIA

a) 180 b) 175 c) 183 d)188

Answer : a) 180

Word 'LETTER' has 6 letters. 'E' is repeated twice and 'T' is repeated twice,

Therefore, number of rearrangements = 6! / (2! x 2!) = 180

Question 3

Consider a word APPLE. Now, if 'A' is to be retained as first letter always, how many possible arrangements are possible.

a) 7 b) 8 c) 9 d) 12

Answer : d) 12

Since A has to be retained as first letter always, the number of possible arrangement out of PPLE will be our answer. In 'PPLE', letter 'P' occurs twice.

Therefore, number of words that can be formed out of 'APPLE' by retaining A as first letter = 4!/2! = 12

Question 4

Find the total number of words that can be made out of the letters of the world 'PARAKEET'

a) 10074 b) 10078 c) 10085 d) 10080

Answer : d) 10080

Word PARAKEET has 8 letters. Letters A and E are repeated twice.

Therefore our answer = 8!/(2! x 2!) = 10080


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