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In how many of the permutations of 10 things taken 4 at a time will 

(i) one thing always occur, (ii) never occur?

1 Answer

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Best answer

(i) Keeping aside the particular thing which will always occur, the number of permutations of 9 things taken 3 at a time is 9P3. Now this particular thing can take up any one of the four places and so can be arranged in 4 ways. Hence the total number of permutations = 9P3 × 4 = 9 × 8 × 7 × 4 = 2016. 

(ii) Leaving aside the particular thing which has never to occur, the number of permutations of 9 things taken 4 at a time is 9P4 = 9 × 8 × 7 × 6 = 3024.

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