Question

There are three buckets, each with 8 different values (A, B, C, D, E, F, G, H). You draw a ball from each bucket. What are the odds that two of the values match? What are the odds that three of the values match?

Please show work.

Answer 1

here total number of ways =all three are different +all three are same+two are matching

total number of ways to drawing from 3 buckets =8*8*8=512

number of ways all three are different =8*7*6=336

number of ways all three are same =8 (as there are 8 different values)

number of ways two are same=512-336-8=168

1)hence odds that two of the values match=ways two are same/ways two are not same=168/(512-168)=21/43

2) odds that three of the values match =ways all three are same/ways not all three are same=8/(512-8)=1/63