1 Three distinguishable dice are rolled. In how many ways can we get a total of 15.
answere is 10
2 Rearrangements :
In a match the column question. Column I has 10 questions and column II has 10 answeres written in arbitary order. In how many ways can a student answere this question such that exactly 6 of his matchings are correct.
answere is 1890
Plz explain in detail.
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2 Answers
62a+b+c = 15
a, b, and c are all less than equal to 6
if a=1/2, b+c=14/13 (which is not possible)
if a=3, b+c=12 1 solution, (b=c=6)
if a=4, b+c=11 2 solution,
if a=5, b+c=10 3 solution, (b=c=6)
if a=6, b+c=9 4 solution, (b=c=6)
total 10 ways [1]
62In a match the column question. Column I has 10 questions and column II has 10 answeres written in arbitary order. In how many ways can a student answere this question such that exactly 6 of his matchings are correct.
answere is 1890
First chose the 6 questions that are correct. 10C6 they can be answered in only 1 way ..
Now you have 4 remaining questions ... which can be answered wrongly in D4=9 ways.. where Dn is the derangement of n
hence the total number of ways is 10x9x8x7/ (1x2x3x4) x 9 = 1890
For derangement try to read http://mathforum.org/advanced/robertd/derangements.html