Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Asked by Aaryan | 1 year ago |  132

##### Solution :-

Here, it is clear that 3 things are already selected and we need to choose (r – 3) things from the remaining (n – 3) things.

Let us find the no. of ways of choosing (r – 3) things.

Number of ways = (No. of ways of choosing (r – 3) things from remaining (n – 3) things)

n – 3Cr – 3

Now we need to find the no. of permutations than can be formed using 3 things which are together. So, the total no. of words that can be formed is 3!

Now let us assume the together things as a single thing this gives us total (r – 2) things which were present now. So, the total no. of words that can be formed is (r – 2)!

Total number of words formed is:

n – 3Cr – 3 × 3! × (r – 2)!

The no. of permutations that can be formed by r things which are chosen from n things in which 3 things are always together is n – 3Cr – 3 × 3! × (r – 2)!

Answered by Sakshi | 1 year ago

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