First slide

Combinations

Question

The number of ways of selecting 10 balls from the unlimited number of red, green, white and yellow balls, if selection must include 2 red and 3 yellow balls, is

Moderate

A

36
B

56
C

112
D

None of these

Solution

Number of 10 balls selections
= coefficient of x¹⁰ in $(x^{2} + x^{3} + \dots) (1 + x + x^{2} + \dots) (1 + x + x^{2} + \dots) (x^{3} + x^{4} + \dots)$
= coefficient of x⁵ in (1 + x + x² +…)⁴
= coefficient of x⁵ in (1 – x)^–4
$=^{(4 + 5 - 1)} C_{5} =^{8} C_{5} = 56 ways$ .

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