MATH SOLVE

4 months ago

Q:
# A security alarm requires a four-digit code. The code can use the digits 0β9 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)/10P4B.(2C1)(9C3)/10C4C.(10P1)(9P3)/10P4D.(10C1)(9C3)/10C4

Accepted Solution

A:

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 0β9 and the digits cannot be repeated. Β there is only 2 numbers which are greater than 7 i.e. 8 and 9. β΄ 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].

Step-by-step explanation:Given:A security alarm requires a four-digit code. The code can use the digits 0β9 and the digits cannot be repeated. Β there is only 2 numbers which are greater than 7 i.e. 8 and 9. β΄ 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].