# The no. Of six digit number that can be formed from tje digits 0,1,2,3,4,5,6&7 so that digits do not repeat and the terminal digits are even

Ankit Jaiswal
165 Points
6 years ago
the total number form which the 6 digit number should be made are 8
out of which 4 are even (0,2,4,6) and these are to be arranged in the terminal points (end points)
hand hence we have to arrange 4 numbers in 2 places (even             even)
hence total numbers of ways we can do this are 4!/(4-2)! = 4*3 = 12
now we have 12 cases with terminal points occupied with two numbers
so we have 4 places remaining with 6 numbers remaining and the number of ways we can do this are
6!/(6-4)! = 6*5*4*3 = 360
hence we have 360 solutions in each case and there are total 12 cases
therefore the total number of 6-digit number that satisfies our condition =
360*12 = $4320$
Ankit Jaiswal
165 Points
6 years ago
T Jahnavi
40 Points
6 years ago
Sir but the answer is 720.......................................................................................................................
Ankit Jaiswal
165 Points
6 years ago
OOH I am sorry for a mistake
Actually I considered that all numbers can occupy first position ( THIS                ) but it cannnot be occupied by 0
so only the number of cases will be affected
that is the first place will have 3 possible cases(2,4,6) and last place will aslo have 3 possible cases(0,2,4,6 out of which oneis already in first place)
so our cases reduces to 3*3 = 9 instead of  12
but then also the answer will be 360*9 =$3240$

and please don’t call me sir.

Ankit Jaiswal
165 Points
6 years ago
i think that the answer will be 720
Ankit Jaiswal
165 Points
6 years ago
i think that the answer will be 720
only is “0” is not incuded

And for that question the solution will be
let the number be
a b c d e f (say)
a = 3 numbers possible (2,4,6)
f = 2 numbers possible (2,4,6 out of which one has occupied “a”)
and then it goes on decreasing

b = 5 numers possible
c = 4 numbers possible
d = 3 numbers possible
e = 2 numbers possible
and hence the answer should be
3*2*5*4*3*2 =$720$

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