Question

Find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated .How many of these will be even

Answer 1

nPr=n!(n−r)!nPr=n!(n−r)!

Out of 5 digits 4 digit numbers are to be formed

Such numbers are 5P45P4

5P4=5!(5−4)!5P4=5!(5−4)!

=5!1!=5!1!

=5×4×3×2=5×4×3×2

=120=120

When 2 is at unit's place ,then remaining three places are filled in 4P34P3ways

4P3=4!(4−3)!4P3=4!(4−3)!

=4×3×2=4×3×2

=24=24

When 4 is at units place,then 4 digit numbers are again =24

∴∴ Even 4 digit numbers =2×242×24

⇒48⇒48