1Anyone watching it ?????
The no. of ways in which a score of 11 can be made from a throw by 3 persons, each throwing a die once is :
A)45
B)18
C)27
D)68
Ans : C
NO USE OF MULTINOMIALS PLEEEEEEAAAASE
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11 Answers
62if you think closely, this is the same as teh number of ways to get 7 by the throw of dice by 3 ppl
This will be a bit dirty counting.. but i hope this observation makes the question slightly simpler .. (at least psychologically :D)
62so the number of ways to get 11
for each dice get 7-i instead of i
so there is a one one onto relation between the number of ways you can get 11 and the number of ways you can get 21-11 = 10
(sorry hadbadi me gadbadi :P)
1Nishant Bhaiyaaaaaaaaaaaaaaaaaaa
calling for help.......!!!!!!
106The no. of ways in which a score of 11 can be made from a throw by 3 persons, each throwing a die once is
x11 in (x1+x2 + ..+x6)3
= x8 in (1-x6)3(1-x)-3
= x8 in (1-3x6)(1-x)-3
= 10C8 -3*4C2
= 45 - 18
= 27
Now for non-multinomial method
suppose u fix that one person gets 6. then the other two persons can get (1,4) (2,3) so total no. of ways = 2*3!
Now let one person get 5. Then other two can get (1,5) (2,4) (3,3) so total no. of ways = 2.3!/2! + 1.3!
Now let one person get 4. Then other two can get (1,6) (ignored as already counted) (2,5) (ignored as already counted) (3,4) so total no. of ways = 3!/2!
So total = 27
Now why havent i considered when one person gets 3 or 2 or 1?
IT is because if one gets 3 then others can get (2,6) (3,5) (4,4) which are all considered above.
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