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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 41 of 41
Marks: +1, -0
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together ?
Solution:  
The total no. of letters in the word ASSASSINATION = 13, in which there are 3A’s, 4S’s, 2N’s and 2I’s.
When all S’s are taken together then take it as one object. Thus, we have a total of (9 + 1) letters.
∴ Required no. of words = 10!36!2!2!\frac{10!}{36!\,2!\,2!} = 10×9×8×7×6×5×42×2\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{2 \times 2} = 151200
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