Question

How many numbers of at mose three different digits can be formed from the integer 1,2,3,4,5,6.​

Answer 1

156 numbers

Explanation:

If the digits have to be at most 3, then we have 3, 2 and 1 digit.

using permutation n! /(n-k)!

Where n is no of objects

k is no to be used

For 3, 6!/(6-3)!

6*5*4*3*2*1/3*2*1 = 120

For 2,

6!/(6-2)!

6*5*4*3*2*1/4*3*2*1 = 30

For 1,

6!/(6-1)!

6*5*4*3*2*1/5*4*3*2*1 = 6

Total, 120 + 30 + 6 = 156

Answer 2

The answer is 1920, right? Here is how-

The numbers must contain at least three digit and can go above that which means the answer has 3 4 5 and 6 digits all together.

For three digits , there will be 6*5*4 = 120

For 4 Digits, There will be 6*5*4*3=360 possible numbers

For 5 digits , there will be 6*5*4*3*2 = 6! = 720

For 6 digits, there will be 6*5*4*3*2*1 = 6! = 720

<Note- the digits are non repeating as the question said it to be “different digits” >

Now add them up = 120+360+2*720 = 1920

Explanation: