In how many different ways can the letters of | vedclass

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(D) The word '$BANKING$' consists of $7$ letters: $B, A, N, K, I, N, G$.There are $2$ vowels $(A, I)$ and $5$ consonants $(B, N, K, N, G)$.Since the v

Vedclass · Accepted Answer

$720$

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(D) The word '$BANKING$' consists of $7$ letters: $B, A, N, K, I, N, G$.There are $2$ vowels $(A, I)$ and $5$ consonants $(B, N, K, N, G)$.Since the vowels must come together,we treat the group $(AI)$ as a single unit.Now,we have the units: ${B, N, K, N, G, (AI)}$.This gives us $6$ units to arrange,where the letter '$N$' repeats $2$ times.The number of ways to arrange these $6$ units is $\frac{6!}{2!} = \frac{720}{2} = 360$.Within the group $(AI)$,the $2$ vowels can be arranged among themselves in $2! = 2$ ways.Therefore,the total number of arrangements is $360 	imes 2 = 720$.

In how many different ways can the letters of the word '$BANKING$' be arranged so that the vowels always come together?

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