Question

Hlo Guys

Find the number of numbers between 300 and 3000 that can formed with the digits 0, 1, 2, 3, 4, and 5 , no digit being repeated in any number .

Answer 1

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Solution :- Any number between 300 and 3000 must be 3 or 4 digits .

$\bf{case - 1}$
When number is 3 digits

Hundred place can be filled up by anyone of the three digits 3, 4, and 5 in 3 ways.

remaining two place can be filled up by remaining five digits in 5P2 ways.

•°• Number of numbers formed in this case

= 3× 5P2 = 3 × 5!/3! = 60

$\bf{case - 2}$
when number is of 4 digits

Thousand place can be filled up by any of 2 digits 1, 2 in 2 ways

Remaining 3 digits can be filled up by remaining five digits in 5P3 ways

number of numbers formed = 2× 5P3 = 2×5!/2! = 120

•°• Required number = 60 + 120 = 180 answer ..

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