shallow9323 wrote:

Bunuel wrote:

A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126

B. 1/120

C. 1/24

D. 4/25

E. 1/2

Kudos for a correct solution.

Please let me know if my logic is correct

I looked at as.

first, total ways to select for all boys and girls,

that is, 10!/(5!*5!)= 252

then there are one two way girls can have all same colors, either white or black.

Therefore, total favorable outcomes/total outcomes = 2/252= 1/126

Dear

shallow9323Your logic is perfectly correct!

For the benefit of other students reading this thread, this alternate approach is described in detail below:

Total number of ways in which the 5 girls can select 5 balls out of 10 balls = 10C5 = 10!/(5!*5!) = 252

(Note: Once the girls select 5 balls, the remaining 5 balls are automatically selected for boys)

The number of ways in which 5 girls can select 5 white balls = 5C5 = 1 (because there are only 5 white balls and all of them have to be selected)

The number of ways in which 5 girls can select 5 black balls = 5C5 = 1

So, number of favorable cases = (No. of ways to select 5 White balls) + (No. of ways to select 5 black balls) = 1 + 1 = 2

So, probability of Event = 2/252 = 1/126

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