Ten identical boxes of dimensions 
are stacked flat on top of each other, with the orientation of each box being independent and random. If 
is the probability that the height of the stack is 
and 
, find 
. All units are in feet.
are stacked flat on top of each other, with the orientation of each box being independent and random. If is the probability that the height of the stack is and , find . All units are in feet.
well x,y,z be number of 2,3,5 as the hieght
ReplyDeleteso x+y+z=10
and we need the case where 2x+3y+5z=31
now prob is m/n total cases possi are 12C2 tht is 66
of this i only want those where sum is 31
now since rhs is odd means...one of 3 or 5 is odd while other is even
only twocases
x,y,z = (1,8,1) and (3,5,2)
so m/n = 2/66 or 1/33
since gcd is 1
m=1
now am sure of the method.. mabye may make a mistake with the number of cases :)
anyways cheers
one mroe case wld be there... of (5,3,2)
ReplyDeleteso well even then m/n=3/66 or 1/22
1/11
ReplyDeletesrry 1/22
ReplyDeleteI have a doubt
ReplyDeleteShould the denominator be
12C2 or 3^10
rahul let me know that
well the Q is abt the final hieght that is got...
ReplyDeletethat means say 2+3+5 = 10 also 3+2+5 =10 both are the same and not two diff cases.... as here am concentrating on the number of times each distinct value is repeated... and not the permutations whithin them.
but yes if u take that each case in itself is diff.. then given those three cases... permute them... with p alike of one type...q of the second and r of the third...
(p+q+r)!/p!*r!*q!