Question:
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?
Updated On: Oct 21, 2023
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Solution and Explanation
In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once.
Since all the words have to be arranged in such a way that all the Ss are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for 10 objects.
These 10 objects in which there are 3 As, 2 Is, and 2 Ns can be arranged in \(\frac{10!}{3!2!2!}\) ways.
Thus, required number of ways of arranging the letters of the given word
\(=\frac{10!}{3!2!2!}=151200\)
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Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
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Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
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