permutation and combination

[shruti290Participant]

q1.)the number of numbers divisible by 3 tht can be formed by four different even digits is?
q2.)the no of 4 digit no tht can be made with the digits 1,2,3,4 and 5 in which at least 2 digits are identical?

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  shruti290Quote

[rohit pandeyParticipant]

for q2
at least 2 digits same means
we take cases for
1.2 same digits
2.3 same digits
3.4 same digits

and add them up

for case 1-5*4*3*2/2!
for case 2 – 5*4*3*2/3!
for case 3 – 5*4*3*2/4!
now add all of them up
this is a probable solution

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  rohit pandeyQuote

[abhisheksharma12593Participant]

atleast 2 are identical means either 2 are identical or 3 are identical or 4 are identical
no of ways if 2 are identical are 5*4*3*2/2!
no of ways if 3 are identical are 5*4*3/3!
no of ways if 4 are identical are 5*4*3*2/4!
adding all three we get 60+20+5=85 ways
our answers are same but i didn’t follow youe method rohit

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  abhisheksharma12593Quote

• This reply was modified 5 years, 4 months ago by  abhisheksharma12593.

[abhisheksharma12593Participant]

*CORRECTION TO ABOVE REPLY
atleast 2 are identical means either 2 are identical or 3 are identical or 4 are identical
no of ways if 2 are identical are 5*4*3*2/2!
no of ways if 3 are identical are 5*4*3*2/3!
no of ways if 4 are identical are 5*4*3*2/4!
adding all three we get 60+20+5=85 ways
our answers are same but i didn’t follow your method rohit
what you are saying is that either 1,2 or 2,3 or 3,4 are identical…plz explain this

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  abhisheksharma12593Quote

[rohit pandeyParticipant]

for q 1

even digits are 0 , 2 , 4 ,6 ,8

so probable 4 digits are 1.0246=0+2+4+6=12
2.2468=2+4+6+8=20
3.4680=4+6+8+0=18
4.6802=6+8+0+2=16
5.8024=8+0+2+4=14

only option 1 and option 3 is divisible by 3

so permutation of option1=4!-3!
( we do -3! factorial because we need 4 digit numbers and thus we fix 0 at fourth place and form permutations and subtract it from total permutations}
and
permutation of option2=4!-3! {same thing again}
this is a probable answer

where did you get this question?

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  rohit pandeyQuote

[shruti290Participant]

i did not follow what u said and the correct ans is 505 i forgot to mention and i got it
basically the question says tht atleast 2 didigts are identical which is just another way of saying tht at least one digit is repeated therefore the answe is
5^4-5!
that is the total no of ways- no digit repeated

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  shruti290Quote

[abhisheksharma12593Participant]

i didn’t get this at all…….let admin come to rescue!!!

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  abhisheksharma12593Quote

[shruti290Participant]

the correct answer is 36 and yours is 18

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  shruti290Quote

[shruti290Participant]

Why did u take o ?
And tell me one thing it says “the no of numbers” so shouldn’t we take the one digit two digit three and four digit no’s As well and since it says diff even do digits therefore we cannot exceed beyond four digits ?

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  shruti290Quote

[adminKeymaster]

For q1, Rohit is right.. and Shruti, his answer is 36 indeed (not 18)

For q2, Shruti is right
#ways at least 2 identical = total ways – #ways none identical
…this is the same approach of using the complement, which is often easier

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  adminQuote

[shruti290Participant]

but sir why did he take 0?

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  shruti290Quote

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