A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.

Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?

StartFraction (2 P 1) (9 P 3) Over 10 P 4 EndFraction
StartFraction (2 C 1) (9 C 3) Over 10 C 4 EndFraction
StartFraction (10 P 1) (9 P 3) Over 10 P 4 EndFraction
StartFraction (10 C 1) (9 C 3) Over 10 C 4 EndFraction

The answer is C

Explanation: Given:A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.  

there is only 2 numbers which are greater than 7 i.e. 8 and 9. ∴ there is 2 possibility for first place.

For the remaining 3 digits there is 9 possibilities (including 1 which would left after choosing 1 from first place )

No of ways for the alarm code beginning with a number greater than 7= 2 P 1 x 9 P 3

Total ways of code with 4 digits= 10 P 4. Hope this helps :)