September 2021 brain puzzler solution

There are 10 books to choose from on a reading list. Mr. Lee would like his students to read any 5. Tameka chooses 5 books randomly as does Nadeem. Find the probability there are exactly two books they both choose.

10 choose 5 = 10 C 5 = 252
There are 252 ways to choose 5 books out of 10.

Tameka needs to pick 2 books from Nadeem’s list and 3 that are not on his list.

There are  10 ways for Tameka to choose 2 of the 5 books on Nadeem’s list. 5C2
From the remaining  5  books that aren’t on Nadeem’s list, there are 10 ways for her to choose 3 of those using 5C3.

10 x 10 so there are 100 possible combinations for the 2 books out of the total 252. 100/252 can be simplified to 25/63.

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