Question -
Answer -
Here, it is clear that3 things are already selected and we need to choose (r – 3) things from theremaining (n – 3) things.
Let us find the no. ofways 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 findthe 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 thetogether things as a single thing this gives us total (r – 2) things which werepresent now. So, the total no. of words that can be formed is (r – 2)!
Total number of wordsformed is:
n – 3Cr – 3 × 3! × (r – 2)!
∴ The no. ofpermutations that can be formed by r things which are chosen from n things inwhich 3 things are always together is n – 3Cr – 3 ×3! × (r – 2)!