Permutations and combinations Please solve the following 33. The 50 states are t

Question

Permutations and combinations

Please solve the following

33. The 50 states are to be ranked in a certain order. How many possible orders are there? In how many ways can the top ten basketball teams be ranked? 35. How many arrangements of the numbers 1,2,7,8,9 are possible if exactly five numbers are used with no repetition and order is unimportant? 36. How many arrangements of the numbers 1,2,7,8,9 are possible if exactly five numbers are used with no repetition and order is important? 37. How many arrangements of the numbers 1,2,7,8,9 are possible if exactly five numbers are used with repetition and order is unimportant?

Explanation / Answer

33) The number of orders of 50 states is equal to the number of permutations of 50 items that is computed as: 50!

Therefore 50! is the required answer here.

34) This is again done in the same way, number of permutation of items is given as: 10!

Therefore 10! is the required answer here.

35) Here there is only 1 arrangement possible as we have to select all 5 of the 5 given numbers and there is only one way to do so. Also here there wont be permuations as order is not important here.

Therefore 1 is the required answer here.

36) This is the same question as above but order of the 5 numbers is also important here. Therefore the number of permutations here would be given as: 5! = 120

Therefore 120 is the required answer here.

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