A box contains 5 diffrents red and 6 diffrent while balls.In how many ways can 6 balls be so that are atleast two balls of each colour?

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Solution

5-R 6-w All diffrents possible cases.
$4 r_{1} 2 w$
$3 R_{1} 3 w$
$2 R_{1}, 4 w$
No .of ways= $5 C_{4} \times 6 c_{2} + 5 C_{3} \times 6 C_{3} + 5 C_{2} \times 6 C_{4}$
$= 5 \times 15 + 10 \times 20 + 10 \times 15$
$= 75 + 200 + 150$
$= 425$

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A box contains 5 diffrents red and 6 diffrent while balls.In how many ways can 6 balls be so that are atleast two balls of each colour?

5-R 6-w All diffrents possible cases.4r12w3R13w2R1,4wNo .of ways=5C4×6c2+5C3×6C3+5C2×6C4 =5×15+10×20+10×15 =75+200+150 =425

5-R 6-w All diffrents possible cases.
$4 r_{1} 2 w$
$3 R_{1} 3 w$
$2 R_{1}, 4 w$
No .of ways= $5 C_{4} \times 6 c_{2} + 5 C_{3} \times 6 C_{3} + 5 C_{2} \times 6 C_{4}$
$= 5 \times 15 + 10 \times 20 + 10 \times 15$
$= 75 + 200 + 150$
$= 425$