Chapter 10.5, Problem 76E

To determine

To calculate:

Numbers of integers greater than $1$ than $999$ but not greater than $4000$ .

Answer to Problem 76E

Numbers of integers greater than $1$ than $999$ but not greater than $4000$ is $375$ .

Explanation of Solution

Given information:

Integers can be formed with $0,1,2,3,4$ .

Repetition is not allowed.

Calculation:

The number greater than $999$ is $1000$ . The largest number is $4000$ .

To find the possible number of integers that can be formed between $1000$ and $4000$ with the digits given are $0,1,2,3,4$ .

So, the required numbers of integers are given as below,

Number of integers is calculated as,

  $=\left(C_{1^{st}}\right).\left(C_{2^{nd}}\right).\left(C_{3^{rd}}\right).\left(C_{4^{th}}\right)$

Where,

  $C_{1^{st}}=$ Choices for first digit.

  $C_{2^{nd}}=$ Choices for second digit.

  $C_{3^{rd}}=$ Choices for third digit.

  $C_{4^{th}}=$ Choices for forth digit.

  $\begin{array}{l}=\left(C_{1^{st}}\right).\left(C_{2^{nd}}\right).\left(C_{3^{rd}}\right).\left(C_{4^{th}}\right)\\ =\mathrm{3.5.5.5}\\ =375\end{array}$

Hence, answer is $375$ .