Chapter 13.2, Problem 2CYP

(a).

To determine

The possible identification number.

Answer to Problem 2CYP

The possible identification number is 5040.

Explanation of Solution

Suppose,

Total possible digits = n

Identification number contains r digits.

So,

The probability of r,

  $P=\frac{n!}{\left(n-r\right)!}$

Therefore,

In the given question,

n = 10

r = 4

So,

Probability of 4-digit identification number,

  $P\left(4-\text{digit}\text{number}\right)=\frac{10!}{\left(10-4\right)!}=\frac{10!}{6!}=10\times 9\times 8\times 7=5040$

(b).

To determine

The probability of number 4213.

Answer to Problem 2CYP

The probability of number 4213 is 1/5040.

Explanation of Solution

Total possible 4-digit identification number = 5040

So,

Probability of 4213 is,

  $P\left(4213\right)=\frac{1}{5040}$

Therefore,

The probability of 4213 is 1/5040.