Question

5. How many two digit numbers less than 100 can be formed with the digits 1, 3, 5, 7, 9
when the digits may be repeated ?​

Answer 1

Answer:

45 two digit numbers less than 100 can be formed with the digits 1, 3, 5, 7, 9

when the digits may be repeated.

Step-by-step explanation:

There are 5 choices and we have fill in two places.

It means,

Unit digit can be filled in 5 ways, since repeatition is allowed, tens too can be filled in 5 ways.

So, for each number on tens place, we have 5 choices for units place.

In this manner, possible ways are -

→ 1(1+1+1+1+1) + 1(1+1+1+1+1) + upto 5 time

→ 5 + 5 + 5 + 5 + 5

→ 5 * 5

→ 25

25 digits can be formed.

So,

Required digits are 2 * 25 - 5(repeated no. Like. 11,33,etc) = 50 - 5 = 45

Method 2 -

This forms an AP, first term = 11, last = 99 and d = 2

→ 99 = 11 + ( n - 1 )2

→ 88 / 2 = n - 1

→ 44 + 1 =n

→ 45 = n

Possible ways = 45