(A) We know that $_{n-1}P_r = \frac{(n-1)!}{(n-r-1)!}$ and $_{n-1}P_{r-1} = \frac{(n-1)!}{(n-r)!}$.Substituting these into the expression:$_{n-1}P_r +

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(A) We know that $_{n-1}P_r = \frac{(n-1)!}{(n-r-1)!}$ and $_{n-1}P_{r-1} = \frac{(n-1)!}{(n-r)!}$.Substituting these into the expression:$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \frac{(n-1)!}{(n-r-1)!} + r \cdot \frac{(n-1)!}{(n-r)!}$$= \frac{(n-1)! \cdot (n-r)}{(n-r)!} + \frac{r \cdot (n-1)!}{(n-r)!}$$= \frac{(n-1)!}{(n-r)!} \cdot (n - r + r)$$= \frac{(n-1)! \cdot n}{(n-r)!}$$= \frac{n!}{(n-r)!} = _nP_r$

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \dots$

A
$_nP_r$
B
$_{n-1}P_r$
C
$_nP_{r-1}$
D
$2 \cdot _nP_r$

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

The number of arrangements of the letters of the word $SALOON$,if the two $O$'s do not come together,is

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How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?

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Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the vowels never occur together?

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If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

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The number of integers greater than $3000$ that can be formed by using any number of digits from the set $\{0, 1, 2, 3, 4, 5\}$ without repetition is:

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$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \dots$

Similar Questions

The number of arrangements of the letters of the word $SALOON$,if the two $O$'s do not come together,is

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Find the number of arrangements of the letters of the word $INDEPENDENCE$. In how many of these arrangements do the vowels never occur together?

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