Question

How many four-digit numbers can be formed with the digits $3,5,7,8,9$ which are greater than $8000$, if repetition of digits is not allowed?

Answer 1

Available digits for filling any place $=\{3,5,7,8,9\}$

Since, the number has to be greater than $8000$,

Thousand's place can be filled by only two digits, (i.e., 8 and 9)

So, number of ways of filling the thousand’s place $=2$

Now, number of ways of filling the hundred’s place $=4$

[Since the repetition of the digits is not allowed.]
Number of ways of filling the ten’s place $=3$
Number of ways of filling the unit’s place $=2$

[By using the fundamental principle of multiplication]

$\therefore$ Total numbers that can be formed

$=2\times 4\times 3\times 2$

$=48$