In how many ways can the letters of the word | vedclass

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Question

(A) The word '$ALGEBRA$' contains $7$ letters,where '$A$' appears $2$ times and all other letters are distinct.Total number of arrangements $= \frac{7

Vedclass · Accepted Answer

$1800$

Vedclass · Answer

(A) The word '$ALGEBRA$' contains $7$ letters,where '$A$' appears $2$ times and all other letters are distinct.Total number of arrangements $= \frac{7!}{2!} = \frac{5040}{2} = 2520$.To find the number of arrangements where both '$A$'s come together,we treat the two '$A$'s as a single unit '$AA$'. Now,we have $6$ units to arrange: ${AA, L, G, E, B, R}$.The number of arrangements where both '$A$'s are together $= 6! = 720$.The number of ways such that both '$A$'s do not come together = (Total arrangements) - (Arrangements where both '$A$'s are together).Required number of ways $= 2520 - 720 = 1800$.

In how many ways can the letters of the word '$ALGEBRA$' be arranged when both $A$ do not come together?

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