Determine the following regarding number of ways things can occur. 10.3 Possible

Question

Determine the following regarding number of ways things can occur. 10.3 Possible lottery number if each lottery ticket purchaser select a six digit number with digit 0 through 9 allowed. 10.4 Number of unique orderings without replacement of nine marbles if they include 4 identical red, 3 identical white, and 2 identical blue Determine the following regarding number of ways things can occur. 10.3 Possible lottery number if each lottery ticket purchaser select a six digit number with digit 0 through 9 allowed. 10.4 Number of unique orderings without replacement of nine marbles if they include 4 identical red, 3 identical white, and 2 identical blue

Explanation / Answer

10.3

There are 10 possibilities (0 to 9) for each of the 6 digits.

Thus, there are 10*10*10*10*10*10 = 1,000,000 possibilities [ANSWER: 1,000,000]

10.4

The number of permutations of n1, n2, n3 like objects on a line is

N(n1, n2, n3) = (n1 + n2 + n3)! / [n1! n2! n3!]

Thus,

N(n1, n2, n3) = 9!/[4!3!2!] = 1260 orderings [ANSWER: 1,260]

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