Directions : Type in your answer in the input box provided below the question. There are n distinct balls in a bag. If the number of ways of selecting five balls from the bag is twice the number of ways of choosing two balls from the bag, find the value of n.

Using the combination formula, selecting r items from n distinct items is calculated as nCr equals n factorial divided by (r factorial times (n minus r) factorial). The problem gives the equation nC5 equals 2 times nC2, which expands to n factorial divided by (120 times (n minus 5) factorial) equals 2 times n factorial divided by (2 times (n minus 2) factorial). By cancelling n factorial and rearranging the terms, we get (n minus 2) factorial equals 120 times (n minus 5) factorial, which simplifies to (n minus 2) times (n minus 3) times (n minus 4) equals 120. Testing the options, if n equals 8, then 6 times 5 times 4 equals 120, satisfying the equation.

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