$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ balls?
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$ \left( \begin{array}{c} m - k \\ n - 1 \end{array} \right)$
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$\left( \begin{array}{c} m - kn + n - 1 \\ n - 1 \end{array} \right)$
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$\left( \begin{array}{c} m - 1 \\ n - k \end{array} \right)$
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$\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$
B
Correct answer
Explanation
Let n = 3 and k = 1
m = 3
According to question, n is number of distinct bags.
Number of balls = 3
Then number of ways balls be placed in 1 ways then, number of ways = 3 x 2 = 6 = <n ways if k = 2
Number of balls = nk = 6
We have chosen at least k balls
Number of ways = one ways