In how many ways can the letters of the word CHEESE be arranged so tha

1.	In how many ways can the letters of the word CHEESE be arranged so that no two E's come together?
Answer» The given word contains 6 letters in which one C, one H, 3E's and one S. Since no two E's come together, first arrange the remaining 3 letters in 3! ways. Then we can find 4 gaps between them. The 3E's can be arranged in these 4 gaps in ⁴P₃/3! = 4 ways. ∴ The number of required arrangements = 3! × 4 = 24

In how many ways can the letters of the word CHEESE be arranged so that no two E's come together?

Answer»

The given word contains 6 letters in which one C, one H, 3E's and one S.

Since no two E's come together, first arrange the remaining 3 letters in 3! ways. Then we can find 4 gaps between them. The 3E's can be arranged in these 4 gaps in ⁴P₃/3! = 4 ways.

∴ The number of required arrangements = 3! × 4 = 24

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In how many ways can the letters of the word CHEESE be arranged so that no two E's come together?

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