Question

The number of 4 digit numbers that can be formed
from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number
contain digit 1 is​

Answer 1

Answer:

750

Step-by-step explanation:

Since we are looking for 4-digit numbers, the first (thousands) digit can't be 0.

Let's split cases:

Case 1: first digit is 1.

In this case, we pick 3 digits in order out of the remaining 7, there are 7⋅6⋅5=210 possibilities.

Case 2: first digit is not 1.

There are 6 ways to choose the first digit (2,3,...,7), 3 ways to place the digit 1 (hundreds, tens, ones), and 6⋅5 (pick 2 in order from the remaining 6 digits) ways to choose the other digits. So there are 6⋅3⋅6⋅5=540 possibilities in this case.

Total

In total, there are 210+540=750 possibilities to choose the number.