How many numbers lying between 10 and 100 can be formed out of the digits 3,0,4,5 and 6 if the repetition is allowed and if repetition is not allowed?
Answers
Answer:
The numbers which are lying between 10 and 100 is 90.
Given: The digits 3, 0, 4, 5 and 6
To find: The number of numbers lying between 10 and 100 can be formed out of the given digits when the repetition is allowed and when repetition is not allowed
Solution: Since we need to find the numbers between 10 and 100, we can omit these two and find the number of numbers from 11 and 99 inclusive. That is, we only need to calculate for two digit numbers.
Case i) If repetition is allowed
The digit in the tens place of the number can be filled in 4 ways by the numbers 3, 4, 5 and 6.
Now, the digit in the ones place of the number can be filled in 5 ways by the numbers 3, 0, 4, 5 and 6.
Hence, the number of numbers that can be formed = 4 × 5 = 20.
Case ii) If repetition is not allowed
The digit in the tens place of the number can be filled in 4 ways by the numbers 3, 4, 5 and 6.
Now, the digit in the ones place of the number can be filled in 4 ways as repetition is not allowed.
Hence, the number of numbers that can be formed = 4 × 4 = 16.
Answer: 20 and 16