Grade 11Magical Mathematics[Interesting Approach]

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

T Jahnavi

9 Years agoGrade 11

7 Answers

Ankit Jaiswal

9 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

9 Years ago

please approve the and

T Jahnavi

9 Years ago

Sir but the answer is 720.......................................................................................................................

Ankit Jaiswal

9 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

9 Years ago

i think that the answer will be 720

Ankit Jaiswal

9 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 = $720$

ARKADEEP DAS

8 Years ago

the answer is simple parmutation

8p3 = 56

so its done

its easy and simple

do u got it it’s nice and simple