Question
How many different numbers of 6-digits can be formed by using digits 4,5,6,7,8,9 (a) no digit being repeated (b) digits may be repeated?
Also, find in case (a) as to how many of them arc odd, when repetition is not allowed?
Solution
Number of digits = 6 (all different)
Number of digits used = 6
(a) Digits are not repeated n = 6, r = 6
Number of permutations = 
Hence, the numbers formed = 720.
(b) The digits may be repeated.
Number of arrangements = 
Hence, numbers formed = 46656.
In part (a), the numbers are to be odd.
Fix box 6 for an odd number.
Number of odd digits = 3 (5, 7, 9)
Number of boxes = 1
n = 3, r = 1
Number of permutations = 
The remaining 5-digits are to be arranged in 5 boxes.
Number of permutations = 
∴ Total numbers formed = 3 x 120 = 360.
