How many numbers between 200 and 600 can be formed by using the digits 1, 2, 3, 4, 5, 6 without repetition? How many of them are even?
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We have to find the count of numbers between 200 & 600 i.e from 201 to 599
without repetition
201
2 _ _
3 _ _
4 _ _
5 _ _
599
For, 2 _ _
In this case we can't use 2 as it is repeated thus we can use 1,3,4,5,6 from the remaining digits to fill the first blank and for the second blank we can use all digits other than 2 and the one filling up the first blank.
We can fill the blanks with 5 x 4 different digits
2 (5) (4) 5 x 4 =20
Similarly other blanks can be filled with 20 different digits
20 x 4 = 80 + 2 = 82
Thus 82 different numbers can be formed between 200 to 600
To find number of even numbers,
2 _ _ should end with 4 as repetition of 2 is not allowed
2 4 4 = 4 x 4 =16
Similarly for other starting digits,
Total even numbers are 4 x (4 x 4) = 64
without repetition
201
2 _ _
3 _ _
4 _ _
5 _ _
599
For, 2 _ _
In this case we can't use 2 as it is repeated thus we can use 1,3,4,5,6 from the remaining digits to fill the first blank and for the second blank we can use all digits other than 2 and the one filling up the first blank.
We can fill the blanks with 5 x 4 different digits
2 (5) (4) 5 x 4 =20
Similarly other blanks can be filled with 20 different digits
20 x 4 = 80 + 2 = 82
Thus 82 different numbers can be formed between 200 to 600
To find number of even numbers,
2 _ _ should end with 4 as repetition of 2 is not allowed
2 4 4 = 4 x 4 =16
Similarly for other starting digits,
Total even numbers are 4 x (4 x 4) = 64
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