Question

Find the number of arranging 11 distinct objects taken 4 at a time so that a specified object never occurs.

Answer 1

There are 11 distinct objects and 4 objects are arranged at a time.
When one specified object does not occur than 4 things are to be arranged from the remaining 10 things, which can be done in ¹⁰P₄ ways
= 10 × 9 × 8 × 7 ways
= 5040 ways
∴ There are 5040 permutations of 11 distinct objects, taken 4 at a time, in which one specified object never occurs.