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

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.

Answer 2

Step-by-step explanation:

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