(B) The number of ways to distribute $n$ identical items into $r$ distinct boxes such that no box is empty is given by the formula $^{n-1}C_{r-1}$.Her

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(B) The number of ways to distribute $n$ identical items into $r$ distinct boxes such that no box is empty is given by the formula $^{n-1}C_{r-1}$.Here,$n = 8$ and $r = 3$.Substituting the values,we get:$^{8-1}C_{3-1} = ^7C_2$.Calculating the value:$^7C_2 = \frac{7 \times 6}{2 \times 1} = 21$.

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

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In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

A
$5$
B
$21$
C
$3^8$
D
$^8C_3$

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Permutation and Combination

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Definition of combinations, Condition combinations

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MediumAP EAMCET 2021

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$\binom{n}{r} \div \binom{n}{n-1} = \dots$

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DifficultJEE MAIN 2024

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DifficultJEE MAIN 2026

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In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

Similar Questions

The number of integers between $10$ and $10,000$ such that in every integer every digit is greater than its immediate preceding digit,is

In how many ways can $4$ balls be picked from $6$ black and $4$ green colored balls such that at least one black ball is selected?

$\binom{n}{r} \div \binom{n}{n-1} = \dots$

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The number of ways in which $16$ identical oranges can be distributed among $4$ children such that each child gets at least one orange is:

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