IIT JEE , AIEEE Forum - Mathematics , Algebra

Anupamagrawal13a

Seven different lecturers are to deliver lectures in seven periods of a class on a particular day.A,B,C are the three different lecturers.The number of ways in which a routine for the day can be made such that A delvers his lectures before B & B before C, is

a)420

b)120

c)210

Please solve this question with good explaination.

pannaguma

clarification reqd.........
so do you mean A directly just before B, or simply before B?

Anupamagrawal13a

Hey pannaguma the question clearly indicates that "A before B".It does not mean "just before B".The case "just before B" would be a include in the situation.

truly

according to me the answer is coming out to be 840...so if there is a correction thn do tell me.

i did it like this

Fixing C in 7th position:

1 2 3 4 5 6 7
X X X X X X X
A B C .......... B in 1 way and remainng in 4!
      A        C ......... B in 2 ways and remaing in 4!
    A          C ......... .B in 3 ways and remaing in 4!
A            C .......... B in 4 ways and remaing in 4!
A            C .......... B in 5 ways and remaing in 4!
total 4!(1+2+3+4+5) = 360

Fixing C in 6th position:

1 2 3 4 5 6 7
X X X X X X X
   A B C .......... B in 1 way and remainng in 4!
     A      C ......... B in 2 ways and remaing in 4!
   A        C ......... .B in 3 ways and remaing in 4!
A           C .......... B in 4 ways and remaing in 4!

total 4!(1+2+3+4) = 240

Fixing C in 5th position:

1 2 3 4 5 6 7
X X X X X X X
    A B C .......... B in 1 way and remainng in 4!
A      C        ......... B in 2 ways and remaing in 4!
A        C     ......... .B in 3 ways and remaing in 4!

total 4!(1+2+3) = 144

Fixing C in 4th position:

1 2 3 4 5 6 7
X X X X X X X
A B C ......... B in 1 way and remainng in 4!
A      C        ......... B in 2 ways and remaing in 4!

total 4!(1+2) = 72

Fixing C in 3rd position:

1 2 3 4 5 6 7
X X X X X X X
A B C .......... B in 1 way and remainng in 4!

total 4!(1) = 24

Total = 360+240+144+72+24 = 840

But as pannaguma said tht Ajust before B and B just before C then the answer coming out to be 5! = 120....which is one of the options.....so chk out

pannaguma

_A_B_C_
now the 4 can be put in 4ways, 5th in 5 gaps, and so on.
so 4*5*6*7 = 20*42=840.

yes daal mein kuch kaala hai!!!!!!!

Anupamagrawal13a

I forgot to write the third option that was none of these.

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