A die is thrown four times, and the sum of four numbers is 22. Find th

Question

A die is thrown four times, and the sum of four numbers is 22. Find the probability that the second throw was a five. A) 1/10 B) 2/10 C) 3/10 D) 4/10 E) 5/10 Screenshot 2025-10-03 11.57.53.png

Bunuel · Answer

For the sum of four throws to be 22, there are only two possible patterns:

6, 6, 5, 5. The number of arrangements is 4!/(2!2!) = 6 
 6, 6, 6, 4. The number of arrangements is 4!/3! = 4

So there are 6 + 4 = 10 total favorable outcomes.

Now, in how many of these does the second throw equal 5?

From the 6 arrangements of {6,6,5,5}, exactly 3 have a 5 in the second position: (6,5,6,5), (6,5,5,6), (5,5,6,6).

So probability = 3/10.

Answer: C.

P.S. The wording of the problem is not very GMAT-like, as often happens with GMATPoint questions.

Kinshook · Answer

Briickky

A die is thrown four times, and the sum of four numbers is 22. Find the probability that the second throw was a five.

22 = 4*6 - 2

Combination 1 = {6,6,5,5} - 4C2 = 6 cases
Combination 2 = {6,6,6,4} - 4C1 = 4 cases

Total cases = 6+4 = 10

Favorable cases = {5,5,6,6},{6,5,5,6},{6,5,6,5} = 3C1 = 3 cases

The probability that the second throw was a five = 3/10

IMO C

Briickky · Answer

Thanks for the solution and for the sources that you have provided, its really means a lot

A die is thrown four times, and the sum of four numbers is 22. Find th

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A die is thrown four times, and the sum of four numbers is 22. Find th

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