In how many ways can we arrange the five vowels, a, e, i, o & u if :(i

1.	In how many ways can we arrange the five vowels, a, e, i, o & u if :(i) two of the vowels e and i are always together.(ii) two of the vowels e and i are never together.
Answer» (i) Using the formula m!(n – m + 1)! Here n = 5, m = 2(e & i) ⇒Required no. of ways = 2!(5 – 2 + 1)! = 2 × 4! = 48 (ii) No. of ways when e & i are never together = total no. of ways of arranging the 5 vowels – no. of ways when e & i are together = 5! – 48 = 72 Or use n! – m!(n – m + 1)! = 5! – 48 = 72

In how many ways can we arrange the five vowels, a, e, i, o & u if :(i) two of the vowels e and i are always together.(ii) two of the vowels e and i are never together.

Answer»

(i) Using the formula m!(n – m + 1)!
Here n = 5, m = 2(e & i)
⇒Required no. of ways = 2!(5 – 2 + 1)! = 2 × 4! = 48

(ii) No. of ways when e & i are never together
= total no. of ways of arranging the 5 vowels

– no. of ways when e & i are together = 5! – 48 = 72

Or use n! – m!(n – m + 1)! = 5! – 48 = 72

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In how many ways can we arrange the five vowels, a, e, i, o &amp; u if :(i) two of the vowels e and i are always together.(ii) two of the vowels e and i are never together.

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In how many ways can we arrange the five vowels, a, e, i, o & u if :(i) two of the vowels e and i are always together.(ii) two of the vowels e and i are never together.