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Question

The combination coefficient n1Cm denotes -

(a) The number of ways in which n things of which m are alike and rest different can arrange in a circle.

(b) The number of ways in which m different things can be selected out of n different thing if a particular thing is always excluded.

(c) Number of ways in which n different balls can be distributed in m different boxes so that no box remains empty and each box can hold any number of balls.


A

onle option a

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B

only option b

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C

Both options a and b

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D

All a, b and c

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Solution

The correct option is B

only option b


(a) The number of ways in which n things of which p are alike and rest different can arranged in a circle = ((n1)!)m!

(b) The number of ways in which m different things can be selected out of n different thing if a particular thing is always excluded = select m different things from n-1 things = n1Cm

(c) Number of ways in which n different balls can be distributed in m different boxes each box can hold any number of balls = mn

Explanation: 1st ball can be put in any of the m boxes in m ways.

Similarly, 2ndball, 3rd ball,.... can be a put in any of the m boxes in m ways.
So, total number of ways = m x m x m x m.....(n times) = mn


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