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Combination with Restrictions

There are 10 ...

Question

There are 10 persons named $P_{1}, P_{2}, P_{3}, . . . ., P_{10} .$ Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement $P_{1}$ must occur whereas $P_{4}$ and $P_{5}$ do not occur. Find the number of such possible arrangements.

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Solution

Total persons = 10

Number of persons to be selected = 5

Condition = p1 must and p4, p5 must not be there

Remaining number of persons required is 4 out of 10 - 3 = 7

$^{7} C_{4} \times 5!$

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