Question

How many 4 digit numbers contain number 2.

a. 3170

b. 3172

c. 3174

d. 3168?

Answer 1

3168  4 digit numbers contain number 2.

In permutations there is a method for solving problems like these.

If we carefully observe the question, we are required to find the number of 4-digit numbers which include 2!!!

For that we first find number of 4 digit numbers. Then numbers of 4-digit numbers which don't have 2. Then we subtract the second one from first one.

that is  

Number of 4-digit numbers with 2=(Number of 4-digit numbers)-(Number of 4-digit numbers without 2).

So again we will be redirected into permutations.

We have condition that repetition is allowed. We have 10 numbers to be filled in 4 places. Since '0' can't be in thousands place, the number of 4-digit numbers will be 9*10*10*10=9000.

To find number of numbers without 2, we have repetition allowed with 9 numbers in 4 places. Since '0' can't be in first place, number of 4-digit numbers without '2' will be 9*9*9*8=5832

So as said earlier the answer will be 9000–5832=3168.

Answer 2

Answer:

Step-by-step explanation: