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Let’s count. Collections

Let's count. Collections
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Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

Exercise 1 How many 5 card hands can be formed from a standard 52 card deck? If one randomly chooses a 5 card hand, what is the probability that all the cards belong to the same suit?

Exercise 2. Let (n) be a natural number. Then we have: [sum_{k=0}^nbinom nk=binom n0+binom n1+cdots+binom nn=2^n.]

Hint: The power set (mathcal P(I_n)) of (I_n={1,2,…,n}) has cardinality (2^n). Inside (mathcal P(I_n)) there are sets of cardinality 0, 1, 2, …, n. How many sets of cardinality (k) are in (mathcal P(I_n))?

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Combinatorics: Strategies and Methods for Counting

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