Theory question 105
Permutations and CombinationsFive digit numbers are formed from digits 4, 5, 6, 7 and 8. (a) How many of such numbers can be formed if repetition of digits is (i) allowed (ii) not allowed? (b) How many of the numbers are odd, if repetition of digits is not allowed?
Show the model answer
Model answer
(a)(i) Each of the 5 places can take any of 5 digits: 5⁵ = 3125
(ii) 5 × 4 × 3 × 2 × 1 = 5! = 120
(b) The last digit must be 5 or 7 (2 ways); the other four places: 4! = 24
Odd numbers = 2 × 24 = 48
Explanation
Fill the units place first when the number must be odd.