Find the number of ways of arranging the letters of the word MISSING s

1.	Find the number of ways of arranging the letters of the word MISSING so that the two S' s are together and the two I’s are together.
Answer» In the given word MISSING contains 7 letters in which there are 2I’s are a like, 2S's are alike and rest are different. Treat the 2S's as one unit and 2I’s as one unit. Then we have 3 + 1 + 1 = 5 entities. These can be arranged in 5! ways. The 2S's can be arranged among themselves in 2!/2! = 1 way and the 2I’s can be arranged among themselves in 2!/2! = 1 way. ∴ The number of required arrangements = 5! × 1 × 1 = 120

Find the number of ways of arranging the letters of the word MISSING so that the two S' s are together and the two I’s are together.

Answer»

In the given word MISSING contains 7 letters in which there are 2I’s are a like, 2S's are alike and rest are different.

Treat the 2S's as one unit and 2I’s as one unit. Then we have 3 + 1 + 1 = 5 entities.

These can be arranged in 5! ways. The 2S's can be arranged among themselves in 2!/2! = 1 way and the 2I’s can be arranged among themselves in 2!/2! = 1 way.

∴ The number of required arrangements = 5! × 1 × 1 = 120

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Find the number of ways of arranging the letters of the word MISSING so that the two S' s are together and the two I’s are together.

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