Question

The number of five digited numbers greater than 50,000 can be formed by using digits 0,1,1,5,9 is
A) 48
B) 24
C) 150
D) 30

Answer 1

Here the digits given are 5 and we have to make numbers greater than 50000. So only two numbers can take place of ten thousandth value .those are 5 and 9 because others can make the number of 5 digits but not greater than 50000. So place them and use permutations or combinations.

Complete step by step solution:
Here they have given that the number should be five digited and is greater than 50,000.
So let’s sort the conditions.

1. The digit at ten-thousandth place can only be either 5 or 9.
2. So only four digits can form the remaining combination.
3. Also, note that 1 is the repeated digit.
4. The number of combinations formed by digit 5 will be equal to that of Number of combinations formed by digit 9.
   So, combinations formed by digit 5 $= \dfrac{{4!}}{{2!}}$
   $$
   \Rightarrow \dfrac{{24}}{2} \\
   \Rightarrow 12 \\

$$So, combinations formed by digit 9 will also be 12. The total number of combinations is 24. **So option B is correct.** **Note:** 1) The number formed is 5 digit number. 2) Digits 1 and 0 are not considered because they are already less than 5 and we are bind to form a 5 digit number. 3) 5 and 9 form the same number of combinations because the remaining numbers are the same. **Additional Information:** 1) The combination is used when we need to do selection especially. 2) Like from similar things or dissimilar things, we have to select in different ways, patterns. 3) It is used in conditions of picking balls, picking a card, selecting a committee, forming a team, forming number.$$