Question

Find the number of positive intergers between 6000 and 7000 with no digirs repepated

Answer 1

According to condition ( less than 1000) ,formed number should not contain 4 digit.

If it contain 4 digit it will become more than 1000.

So the answer digits can contain 3, 2 and 1 digit.

Now stick to permutation formula

nPr = n!/(n-r)! Where n=no. of possibility

r=no. of digits

If r=3

5P3= 5×4×3×2!/2! =60

If r=2

5P2 = 5×4×3!/3! =20

If r=1

5P1 =5×4!/4! =5

Total numbers less than 1000 can be formed using the digits 5, 6, 7, 8, 9 if no number of digit is repeated = 5P3+5P2+5P1 =60+20+5= 85