A box contains 10 green balls and 8 yellow balls . In how many ways two balls of the same colour can be drawn ?

dear student,
 the formula for selecting "r" number of objects from "n" number of objects is
nCr =n!/r!(n-r)!
 
Number of ways of selecting two balls from 10 + 8 = 18 balls is 18C2=18!/2!(18-2)!=18*17*16...2*1/2*1(16*15*...2*1)=18*17/2=306/2 =153

similarly.
Number of ways of selecting two green balls from 10 green balls = 10C2 =45

Number of ways of selecting two yellow balls from 8 yellow balls = 8C2= 28
Favorable ways = 45+28=73
Required probability = Favorable ways / Total ways = 73/153

regards.
 
 

 

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9 balls can be drawn same kind
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in 9 ways two balls of same colour can be drawn
 
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