(C) Given that $d(n)$ represents the number of positive divisors of $n$.For a prime number $P$,the divisors of $P^7$ are $P^0, P^1, P^2, P^3, P^4, P^5

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(C) Given that $d(n)$ represents the number of positive divisors of $n$.For a prime number $P$,the divisors of $P^7$ are $P^0, P^1, P^2, P^3, P^4, P^5, P^6, P^7$. Thus,$d(P^7) = 8$.Next,we find $d(8)$. Since $8 = 2^3$,the number of divisors is $3 + 1 = 4$. Thus,$d(8) = 4$.Finally,we find $d(4)$. Since $4 = 2^2$,the number of divisors is $2 + 1 = 3$. Thus,$d(4) = 3$.Therefore,$d(d(d(P^7))) = 3$.

Class 11 Mathematics Permutation and Combination Multinomial theorem, Number of divisors

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For any integer $n \geq 1$,the number of positive divisors of $n$ is denoted by $d(n)$. Then,for a prime $P$,$d(d(d(P^7)))$ is equal to

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Permutation and Combination

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Multinomial theorem, Number of divisors

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