A man makes a payment of $33 using a large numbers of $1 and $5 coins. In how many ways can this be done and what is the probability that at least 20 $1 coins are used.

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The man has to make a payment of $33 using $1 and $5 coins. The different ways in which this can be done are:

  1. 1 $5 coin and 28 $1 coins
  2. 2 $5 coins and 23 $1 coins
  3. 3 $5 coins and 18 $1 coins
  4. 4 $5 coins and 13 $1 coins
  5. 5 $5 coins and 8 $1 coins
  6. 6 $5 coins and 3 $1 coins

In 2 of these at least 20 $1 coins are used.

The probability that at least 20 $1 coins are used in the method of payment is 1/3.

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