Multiple choice

In how many ways can 45 men be allotted to 3 different districts, if the districts are to be covered by 10, 15 and 20 men?

  1. 45P3

  2. 45 ! 10 ! × 15 ! × 20 !

  3. 3 ! × ( 45 ) ! 10 ! × 15 ! × 20 !

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

This is a problem of dividing 45 men into 3 distinct groups of 10, 15 and 20. The formula for dividing n items into groups of size a, b and c is n factorial divided by the product of a factorial, b factorial and c factorial. Applying this, the number of ways is 45 factorial divided by (10 factorial times 15 factorial times 20 factorial). This matches the result of option B.

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