Question

Two boys are trick-or-treating on Halloween, dressed as Challa and Dracula. Mrs. Owens has a bowl with seven different candy bars in it (one Kit-Kat, one Milky Way, one Snickers, one Crunch, one Twix, one Baby Ruth, and one Almond Joy), and she tells the boys that they can each take two candy bars from the bowl. If Challa picks first, how many ways are there for them to select their candy?

Answer 1

Explanation: Challa can pick up the first candy bars in 7 ways (anyone out of the available 7 bars)

Now, Dracula can pick up any of the remaining 6 bars, which can be done in 6 ways

Then, Challa will pick his second in 5 ways and Dracula can pick up his second in 4 ways

Total Number of ways = 7 * 6 * 5 * 4 = 840 ways

What is the catch?

For example, Challa picked first kit-kat and then snickers. Other option, is first snickers and then kit-kat, so we are counting this one case, twice.

Hence, actual number of ways = 840 * 1/2 (Counting twice for challa)* 1/2 (Counting twice for Dracula) = 210 ways.

Note - Post any doubts/queries in comments section.