Sum

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

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#### Solution

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 ^{10}P_{4 }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.

Concept: Concept of Permutations - Permutations When All Objects Are Distinct

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