Question

5. Using only the digits of 1, 4, 5, 8, (a) How many three digit numbers can be formed? (b) How many odd numbers greater than 10 can be formed? (c) How many even number less than 300 can be formed?

Repetition is allowed!

Answer 1

Solution:
Given in the question
Digits are 1,4,5,8
There are 2 digits are odd digits which are 1,5
There are 2 digits are even digits which are 4,8
Solution(a)
We need to calculate number of three digits can be formed
Number of ways to choose First digit = 4
Number of ways to choose second digit = 4
Number of ways to choose third digit = 4
So total number of ways to make three digits = 4*4*4 = 64 Ways
Solution(b)
We need to found odd numbers greater than 10 can be formed
As numbers are greater than 10 so one digit numbers are not allowed
Number of ways to make 2 digit Odd number = 4*2 = 8
Number of ways to make 3 digit Odd number = 4*4*2 = 32
Number of ways to make 4 digit Odd number = 4*4*4*2 = 128
Totan number of ways to make odd numbers greater than 10 = 8+32+128 = 168
Solution(c)
How many even number less than 300 can be formed?
Number of ways to make One digit even number = 2
Number of ways to make two digit even number = 4*2 = 8
Number of ways to make three digit even number but less than 300, First digit can be 1 only because we need to make less than 300, 2nd digit can be anything out of 4 and 3 rd digit should be evne out of 2 = 1*4*2 = 8
Total Even number less than 300 can be formed = 2+8+8 = 18