(A) To distribute $n$ identical items among $r$ distinct recipients such that each recipient gets at least $1$ item,we use the stars and bars method (

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(A) To distribute $n$ identical items among $r$ distinct recipients such that each recipient gets at least $1$ item,we use the stars and bars method (or the formula for positive integer solutions to $x_1 + x_2 + \dots + x_r = n$).Here,$n = 8$ and $r = 3$.The number of ways is given by the formula $\binom{n-1}{r-1}$.Substituting the values,we get $\binom{8-1}{3-1} = \binom{7}{2}$.$\binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21$.

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

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The number of ways of distributing $8$ identical rings to $3$ different girls so that every girl gets at least $1$ ring is

AP EAMCET 2021 All AP EAMCET

A
$21$
B
$120$
C
$^8 P_3$
D
$^8 P_3 - 6$

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Definition of combinations, Condition combinations

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The number of ways of distributing $8$ identical rings to $3$ different girls so that every girl gets at least $1$ ring is

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