Exercise 1: Exactly 3 Heads in 5 Coin Flips — Possible Solution
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GIVEN
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n = 5, k = 3, p = 0.5 (a fair coin)

STEP 1: C(n, k)
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C(5, 3) = 5! / (3! x 2!) = (5 x 4) / (2 x 1) = 10

STEP 2: p^k
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p^3 = 0.5^3 = 0.125

STEP 3: (1-p)^(n-k)
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(1-p)^(5-3) = 0.5^2 = 0.25

STEP 4: COMBINING
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P(X=3) = C(5,3) x p^3 x (1-p)^2
        = 10 x 0.125 x 0.25
        = 0.3125 (31.25%)

WHY THIS WORKS AS AN ANSWER
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Each of the three terms in this chapter's own binomial formula is
computed separately - the number of ways to choose which 3 of the 5
flips landed heads, the probability of any one specific sequence of 3
heads, and the probability of the remaining 2 flips landing tails -
before being multiplied together, matching the chapter's own worked
coin-flip example step by step.