How many number of five digits can be formed without repetition if two three and five always occurs in each number and 0 never occurs
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Step-by-step explanation:
5 digit numbers are to be formed without repetition.
There are 5 places to be filled.
(i) if 2,3 and 5 always occur, 3 places are occupied by these numbers.
It can be arranged in 5P3 ways.
Rest two places(out of 5) can be filled by the rest 7 digits(0,1,4,6,7,8,9)
It can be done in 7P2 ways.
But this includes the cases where 0 is in the beginning. if 0 remains in the beginning, it will be a 4 digit number. so you need to subtract it.
If we keep 0 at first place and form the numbers, total numbers will be = 1× 4P3×6 = 24×6 = 144
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(ii)
if zero never occurs, the five places can be filled by 9 digits (1 to 9)
Number of ways to do it = 9P5
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