Question

Find the total number of ways in which a 3 digit number xyz can be formed from the digits such that x, y, z are in ap

Answer 1

Answer:

Step-by-step explanation:

The solution is relatively simple if you start by picking y first!

when y=1 no solutions

y=2, 2 solutions

y=3, 4 solution

y=4, 6 solutions

y=5, 8 solutions

y=6, 6 solutions

y=7, 4 solutions

y=8, 2 solutions

y=9, 0 solutions..

Add the values 2+4+6+8+6+4+2+0=32

So total number ways are 32.

Answer 2

Given that the Numbers are in A.P

AP stands for Arithmetic Progression.

The basic property of AP is Common Difference. It is possible only if all the numbers are Distinct Numbers.

Now given that x, y, z are in AP.

∵ Because we have to make a 3-digit number like "147", so we have to use all the 3 digits.

⇒  Case 1 :-  According to the statement, if we have to arrange x, y, z given in AP  as xyz, then it is possible only ONCE.  

⇒ Like 147

⇒  Case 2 :- But if we have to see, how many different 3-digit numbers we can make using x, y, z given in AP, then

                           Total ways = 3! = 6 ways

For example : Let the numbers are  1 , 4 , 7

The possible 3-digit numbers are

                         147 , 174 , 471 , 417 , 714 , 741 are the six possible ways.