New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six...

New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. (a) Do calculations for winning this lottery involve permutations or combinations? why? (b) How many different lottery tickets are possible? (c) Find the probability of winning the jackpot when one ticket is purchased?

Expert Solution

Solution:

A)

Permutations of objects are the arrangements of the objects. In the arrangement, order of objects matters.

For example if we have three objects M, N, O, there are total 6 arrangements of objects are possible MNO, MON, OMN, NMO, NOM, ONM. Total number of permutation of r objects out of n objects is denoted by P and given by

Combination is the selection of r objects out of n different objects and order of the selection of objects does not matter. If there are 3 objects A, B and C and we have to select 2 objects out of three. Then selection AB and BA are same. Total number of combinations of objects out of n objects is denoted nCr by and given by

Since here order of selection of 6 numbers out of 49 numbers does not matter so combination should be used.

Hence, calculations for winning lottery involve combination

Please post remaining as new question... Please

orchestra answered 1 year ago

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New Jersey Pick 6. In the New Jersey Pick 6 lottery game, a bettor selects six...

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