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Find the generating function to denote the number of ways the sum 9 can be acquired while 2 distinguishable fair dice are tossed and the first shows an even number and the second shows an odd number.
Ans: suppose x1 and x2 be the variable denoting the outcomes on the two dice the x1 has values 2, 4, 6 and x2 has 1, 3, 5. Here now polynomial for variable x1 and x2 can be written as (x2 + x4 + x6) and (x + x3 + x5) correspondingly.
So the number of ways sum 9 can be acquired is equal to the coefficient of x9 in the expression (x2 + x4 + x6) (x + x3 + x5). This is equal to 2.
Find out how many words can be formed out of the letters of the word DAUGHTER such that (i) The vowels are all time together. (ii) The vowels occupy even places. Ans:
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