Question

How many vehicle registration plate numbers can be formed with digits 1,2,3,4,5 (no digit being repeated)if it's given that registration number can have 1 to 5 digits? a?

Answer 1

Number plate formed with one digit number = $^5C_{1} \times 1!$

By using the combination formula, $^nC_{r}=\frac{n!}{r!(n-r)!}$

= $\frac{5!}{4! \times 1!}$

= 5.

Number plate formed with two digit number = $^5C_{2} \times 2!$

= $\frac{5!}{3! \times 2!} \times 2!$

= 20.

Number plate formed with three digit number = $^5C_{3} \times 3!$

= $\frac{5!}{3! \times 2!} \times 3!$

= 60.

Number plate formed with four digit number = $^5C_{4} \times 4!$

= $\frac{5!}{4! \times 1!} \times 4!$

= 120.

Number plate formed with five digit number = $^5C_{5} \times 5!$

= $\frac{5!}{5! \times 0!} \times 5!$

= 120.

So, total number of number plates formed = 5+20+60+120+120

= 325.

Answer 2

Answer:

Step-by-step explanation:

Single digit number plates =   5C1 x 1!

Two digit number plates =   5C2 x 2!

Three digit number plates =   5C3 x 3!

Four digit number plates =   5C4 x 4!

Five digit number plates =   5C5 x 5!

Total = (5C1 x 1!) + (5C2 x 2!) + (5C3 x 3!) + (5C4 x 4!) + (5C5 x 5!) = 5 + 20 + 60 + 120 + 120 = 325