a burger chain wants to send codes for a free small drink to the members of its kids club. the coupon code…
a burger chain wants to send codes for a free small drink to the members of its kids club. the coupon code will have one letter, followed by two digits, followed by two letters. the letters r, s, t, and u and the digit 3 will not be used. so, there are 22 letters and 9 digits that will be used. assume that the letters and digits can be repeated. how many such coupon codes can be generated? coupon codes
Answer
Explanation:
Step1: Analyze the number of choices for each position
The coupon - code has a format of one letter, two digits, and two letters. There are 22 choices for each letter position and 9 choices for each digit position.
Step2: Use the counting principle
The counting principle states that if there are (m_1) ways to do the first task, (m_2) ways to do the second task, (\cdots), (m_n) ways to do the (n)th task, then the total number of ways to do all (n) tasks together is (m_1\times m_2\times\cdots\times m_n). For the first letter, there are 22 choices. For the first digit, there are 9 choices. For the second digit, there are 9 choices. For the third letter, there are 22 choices. For the fourth letter, there are 22 choices. The total number of coupon - codes is (22\times9\times9\times22\times22).
Step3: Calculate the result
[ \begin{align*} &22\times9\times9\times22\times22\ =&22\times9^2\times22^2\ =&22\times81\times484\ =&1782\times484\ =&862488 \end{align*} ]
Answer:
862488