Permutation and CombinationHard
Question
The number of non-negative integral solutions of x1 + x2 + x3 + x4 ≤ n (where n is a positive integer) is
Options
A.n+3C3
B.n+4C4
C.n+5C5
D.n+4Cn
Solution
x1 + x2 + x3 + x4 ≤ n
⇒ x1 + x2 + x3 + x4 + y = n
(where y is known as pseudo variable)
Total no. of required solution is
= n + 5 - 1Cn = n+4Cn or n+4C4
⇒ x1 + x2 + x3 + x4 + y = n
(where y is known as pseudo variable)
Total no. of required solution is
= n + 5 - 1Cn = n+4Cn or n+4C4
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