Answer:
The correct expression that can be used to determine the probability of the alarm code beginning with a number greater than 7 is:
StartFraction (2 C 1) (9 C 3) Over 10 C 4 EndFraction.
Step-by-step explanation:
"StartFraction" indicates the start of a fraction.
"(2 C 1)" represents choosing 1 item from 2 items without replacement, which means choosing 1 digit greater than 7 from the available options (8 and 9).
"(9 C 3)" represents choosing 3 items from 9 remaining items without replacement, which means choosing 3 digits from the remaining digits 0-7 (excluding the digit greater than 7).
"Over" indicates division.
"10 C 4" represents choosing 4 items from 10 total items (digits 0-9) without replacement, which represents all possible combinations of a 4-digit code.
"EndFraction" indicates the end of the fraction.
Using combination notation "(n C r)" is appropriate in this case because the order of the digits in the code does not matter and each digit can only be used once (cannot be repeated), which is a characteristic of combinations.