find the number of ways of drawing 9 balls from a bag that has 6 red balls 8 green balls and 7 blue balls so that 3 balls of every colour are drawn
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Step-by-step explanation:
balls =6C3×8C3×7C3
.
Using the formula nCr=n!(n−r)!×r!
, we get
⇒
Required number of ways of drawing the 9 balls =6!(6−3)!×3!×8!(8−3)!×3!×7!(7−3)!×3!
On further simplification, we get
⇒
Required number of ways of drawing the 9 balls =6!3!×3!×8!5!×3!×7!4!×3!
Now, we will find the values of the factorials.
⇒
Required number of ways of drawing the 9 balls =6×5×4×3!3×2×1×3!×8×7×6×5!5!×3×2×1×7×6×5×4!4!×3×2×1
On further simplification, we get
⇒
Required number of ways of drawing the 9 balls =5×4×8×7×7×5
On multiplying these numbers, we get
⇒
Required number of ways of drawing the 9 balls =39200
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