Answer: A is the right answer. The probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].
Step-by-step 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=[tex]^2P_1\times\ ^9P_3[/tex]
Total ways of code with 4 digits=[tex]^{10}P_4[/tex]
Therefore the probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].
