The combination coefficient n−1Cm 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.
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 = ((n−1)!)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 = n−1Cm
(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