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If ten students appear in an examination and 4 of them are [#permalink]
06 Jan 2004, 15:14

If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

If it were a computer adaptive test then it would be 10!

If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

I'm a little confused now, there are only 5 spaces between 6 students. I'm not in my right mind today - stressful day in the markets for me.

If ten students appear in an examination and 4 of them are appearing for mathematics and rest for 6 different subjects, in how many ways can they be seated in a row so that no copying is possible?

I'm a little confused now, there are only 5 spaces between 6 students. I'm not in my right mind today - stressful day in the markets for me.

subtract number of ways in which atleast two are together from the total number of ways.

if 2 are together then we have 4C2 and treating this as one group we have 8 people left so number of ways = 4C2 * (8+1)!
smilarly 3 people together = 4C3 * (7+1)!
and 4 people together = 4C4 * (6+1)!

total ways in which copying takes place =
4C2 * 9! + 4C3 * 8! + 4C4 * 7! = 7! * 465
subtract this from 10!
so we get
7! ( 10*9*8 - 465 ) = 255 * 7!

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