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 are to be taken at a time.

When one particular object will not occur then 4 object are to be arranged from 10 objects which can be done in ¹⁰P₄ ways

= 10 × 9 × 8 × 7

= 5040

∴ In 5040 permutations of 11 distinct objects, taken 4 at a time, one particular object will never occur.