The number of ways of distributing $15$ things to $4$ persons such that each person receives at least two things is

120

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108

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Solution

The correct option is A 120
This problem is equivalent to,
No. of non-negative integral solutions of,
$x_{1} + x_{2} + x_{3} + x_{4} = 15 - 2 \times 4 = 7$
$∴$ No. of required ways $=^{7 + 4 - 1} C_{4 - 1} = 120$

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The number of ways of distributing 15 things to 4 persons such that each person receives at least two things is

The correct option is A 120This problem is equivalent to, No. of non-negative integral solutions of,x1+x2+x3+x4=15−2×4=7∴No. of required ways =7+4−1C4−1=120

The number of ways of distributing $15$ things to $4$ persons such that each person receives at least two things is

The correct option is A 120
This problem is equivalent to,
No. of non-negative integral solutions of,
$x_{1} + x_{2} + x_{3} + x_{4} = 15 - 2 \times 4 = 7$
$∴$ No. of required ways $=^{7 + 4 - 1} C_{4 - 1} = 120$