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Question 26 : How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
_ _ _ _ on the 4 digit 7 has to come before 3
So, 4C2 possibilities for 7 coming before 3 into the spaces
7 ___ 3 ____, 2 numbers are already there and 2 remaining spots we have to fill in
From 8 digits available (Excluding 7 and 3)
So, 8C2 ways of choosing
After choosing two from 8, that two can be placed in any way
For example : 1 and 2 can be arranged as 12 and 21
So, 4C2 × 8C2 × 2
Now we need to subtract the possibility where 0 comes in the first position
0753, So these are in the form 0__ __ __
In this 3 places 7 before 3 can be placed in 3C2 ways and remaining 1 digit
Can be chosen from 7 (Excluding 0,3,7) digits.
3C2 × 7 = 21 numbers
Should subtract 21 from 4C2 × 8C2 × 2
= (6 × 28 × 2) – 21
The question is "How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?"
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