Permutation and CombinationHard
Question
Number of numbers greater than a million and divisible by 5 which can be formed by using only the digits 1, 2, 1, 2, 0, 5 & 2 is -
Options
A.120
B.110
C.90
D.none of these
Solution
For a number to be divisible by 5,5 or 0 should be at units place.
∴ Unit place can be filled by 2 ways
Remaining digits can be filled in
ways.
∴ Total ways =
But these arrangements also include cases where 0 is at millions place 5 at units place, which are undesirable cases
⇒
ways (undesirable )
subtract it from total ways.
∴ Desired ways = 2 ×
= 110
∴ Unit place can be filled by 2 ways
Remaining digits can be filled in
ways.∴ Total ways =
But these arrangements also include cases where 0 is at millions place 5 at units place, which are undesirable cases
⇒
ways (undesirable )subtract it from total ways.
∴ Desired ways = 2 ×
= 110Create a free account to view solution
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