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Tagged: permutation and combination
This topic contains 10 replies, has 4 voices, and was last updated by shruti290 6 years, 1 month ago.

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August 9, 2014 at 8:18 pm #499

August 9, 2014 at 11:15 pm #501
for q2
at least 2 digits same means
we take cases for
1.2 same digits
2.3 same digits
3.4 same digitsand add them up
for case 15*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
rohit pandeyQuote
August 10, 2014 at 12:10 am #503
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
abhisheksharma12593Quote This reply was modified 6 years, 1 month ago by abhisheksharma12593.

August 10, 2014 at 12:24 am #506
*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 didnâ€™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
abhisheksharma12593Quote


August 9, 2014 at 11:47 pm #502
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=14only 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 answerwhere did you get this question?
rohit pandeyQuote
August 10, 2014 at 11:10 am #509
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
5^45!
that is the total no of ways no digit repeated
shruti290Quote
August 10, 2014 at 11:19 am #513


August 10, 2014 at 11:14 am #510

August 10, 2014 at 2:57 pm #518


August 11, 2014 at 12:23 pm #526
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
adminQuote
August 11, 2014 at 4:25 pm #535


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