All the letters of the word ABRACADABRA are a | vedclass

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Question

(D) The word $ABRACADABRA$ contains $11$ letters: $A$ ($5$ times),$B$ ($2$ times),$R$ ($2$ times),$C$ ($1$ time),$D$ ($1$ time).There are $5$ vowels,a

Vedclass · Accepted Answer

$1260$

Vedclass · Answer

(D) The word $ABRACADABRA$ contains $11$ letters: $A$ ($5$ times),$B$ ($2$ times),$R$ ($2$ times),$C$ ($1$ time),$D$ ($1$ time).There are $5$ vowels,all of which are $A$. We treat these $5$ $A$'s as a single unit $(AAAAA)$.Now,we have the following items to arrange: $(AAAAA), B, B, R, R, C, D$.This gives us $7$ items in total,where $B$ repeats $2$ times and $R$ repeats $2$ times.The number of arrangements of these $7$ items is $\frac{7!}{2!2!} = \frac{5040}{4} = 1260$.Since all the vowels are identical $(A)$,there is only $1$ way to arrange them within the unit.

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

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