Question

How many different plates are there that involve 1, 2 or 3 letters followed by 1,

2, 3 or 4 digits?

How many 2 digit or 3-digit numbers can be formed using the digits 1, 3, 4, 5, 6,

8 and 9 if no repetition is allowed?

Answer 1

i.

$$26(10)+26(10)^2+26(10)^3+26(10)^4$$

$$+26^2(10)+26^2(10)^2+26^2(10)^3+26^2(10)^4$$

$$+26^3(10)+26^3(10)^3+26^3(10)^3+26^3(10)^4$$

$$=218886980$$

ii.

$$P(7,2)+P(7,3)=\dfrac{7!}{(7-2)!}+\dfrac{7!}{(7-3)!}$$

$$=42+210=252$$