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The total number of ways of selecting six coins out of $20$ one rupee coins,$10$ fifty paise coins,and $7$ twenty-five paise coins is:

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The least value of $n$ such that ${ }^{(n-1)} C_3 + { }^{(n-1)} C_4 > { }^n C_3$ is:

The least value of the natural number $n$ satisfying $C(n, 5)+C(n, 6)>C(n+1, 5)$ is

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