Exercises

**1.** [*00*] How many ways are there to shuffle a 52-card deck?

**2.** [*10*] In the notation of Eq. (2), show that *p*_{n(n−1)} = *p*_{nn}, and explain why this happens.

**3.** [*10*] What permutations of {1*,* 2*,* 3*,* 4*,* 5} would be constructed from the permutation 3 1 2 4 using Methods 1 and 2, respectively?

**4.** [*13*] Given the fact that log_{10} 1000! = 2567.60464 ..., determine exactly how many decimal digits are present in the number 1000!. What is the *most significant* digit? What is the *least significant* digit?

**5.** [*15*] Estimate 8! using the following more exact version of Stirling’s approximation:

**6.** [*17*] Using Eq. (8), write 20! as a product of prime factors. ...

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