Question

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?

A.(2P1)(9P3)/10P4

B.(2C1)(9C3)/10C4

C.(10P1)(9P3)/10P4

D.(10C1)(9C3)/10C4

Answer 1

Answer: A is the right answer. The probability of the alarm code beginning with a number greater than 7 =
`(^2P_1*\ ^9P_3)/(^(10)P_4)`.

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=
`^2P_1*\ ^9P_3`

Total ways of code with 4 digits=
`^(10)P_4`

Therefore the probability of the alarm code beginning with a number greater than 7 =
`(^2P_1*\ ^9P_3)/(^(10)P_4)`.