A box contains $5$ blue, $6$ yellow and $4$ red balls. The number of ways of drawing $8$ balls containing at least two balls of each colour is: [JEE Main 2026, 5 Apr (Shift 2)]

Question

YESPYQ · Accepted Answer

Correct answer: a) $4100$. The possible selections of balls are: $(2$ blue, $2$ yellow, $4$ red), ( $2$ blue, $4$ yellow, $2$ red), ( $4$ blue, $2$ yellow, $2$ red), ( $3$ blue, $3$ yellow, $2$ red), ( $3$ blue, $2$ yellow, $3$ red) or ( $2$ blue, $3$ yellow, $3$ red) $={ }^5 C_2 \cdot{ }^6 C_2 \cdot{ }^4 C_4+{ }^5 C_2 \cdot{ }^6 C_4 \cdot{ }^4 C_2+{ }^5 C_4 \cdot{ }^6 C_2 \cdot{ }^4 C_2+{ }^5 C_3 \cdot{ }^6 C_3$. ${ }^4 C_2+{ }^5 C_3 \cdot{ }^6 C_2 \cdot{ }^4 C_3+{ }^5 C_2 \cdot{ }^6 C_3 \cdot{ }^4 C_3$ $=150+900+450+1200+600+800 =4100$

A box contains \(5\) blue, \(6\) yellow and \(4\) red balls. The number of ways of drawing \(8\) balls containing at lea…

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