Question

The number of 5 digit numbers greater than 5000 that can be formed by using the digits 0, 1, 1, 5, 9 is
A.48
B.24
C.150
D.30

Answer 1

Hint: Here, we need to find the number of five digit numbers that can be formed using the given five digits. We can use only two digits in the first place as we need to find the numbers greater than 50000. Then we will find the number of 5 digit numbers starting with 5 and then we will find the number of 5 digit numbers starting with the number 9. Then we will add both of them to get the required number.

Complete step-by-step answer:
Here, we need to find the number of five digit numbers that can be formed using the digits 0, 1, 1, 5, 9.
Total number of digits is 5.
Therefore, numbers greater than 50000 will have either 5 or 9 in the first place.
The number of 5 digits numbers formed when we take 5 at the first place $ = \dfrac{{4!}}{{2!}}$
On putting the value of factorials, we get
The number of 5 digits numbers formed when we take 5 at the first place $ = \dfrac{{4 \times 3 \times 2 \times 1}}{{2 \times 1}}$
On further simplification, we get
 The number of 5 digits numbers formed when we take 5 at the first place $ = 12$
Similarly, the number of 5 digits numbers formed when we take 9 at the first place $ = \dfrac{{4!}}{{2!}}$
On putting the value of factorials, we get
The number of 5 digits numbers formed when we take 9 at the first place $ = \dfrac{{4 \times 3 \times 2 \times 1}}{{2 \times 1}}$
On further simplification, we get
 The number of 5 digits numbers formed when we take 9 at the first place $ = 12$
Therefore, total number of 5 digit numbers that can be formed $ = 12 + 12 = 24$
Hence, the correct option is option B.

Note: Since we have used factorials here. So, we need to know its meaning and definition of factorial.
Factorial of any positive integer can be defined as the multiplication of all the positive integers less than or equal to the given positive integers.
Factorial of zero is one.
Factorials are generally used in permutations and combinations problems.
Factorials of negative integers are not defined.