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# Permutations (general)

1.Define and characterize permutations and permutations with repetition.

Solution:

**Permutations**

A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, without repetitions, and not necessarily using all n elements of the given set.

Number of possible permutations:

**Permutations with repetition**

A permutation is an ordered sequence of k elements selected from a given finite set of n numbers, with repetitions, and not necessarily using all n elements of the given set.

Number of possible permutations with repetition:

V*(k,n) = n^{k}

2. From a given set M = {a,b,c,d} enumerate the permutations with and without repetition for k=2. Determine their number.

a) Permutations:

b) Permutations with repetition:

3. There are 7 members in a committee. How many ways are there to choose a chairman, deputy chairman, secretary and a cash keeper?

Permutations, n = 7, k = 4

There are 840 ways of choosing the four officials.

4.Eight students promissed to send a postcard each other. How many postcards did they send together?

Permutations, n = 8, k = 2

The students sent 56 postcards.

5.From how many numbers 240 permutations can be made if the number of elements to be selected is 2?

Permutations, n = x, k = 2

16 numbers are needed.

6.If the number of members increments by 2, the number of possible variations with k=3 increments by 384. How many members are there?

There are 8 members.

7. You have 6 different tickets in your pocket marked with numbers 1-6. How many ways are there to choose 3 of them (considering the order), if

a) the selected ticket is not returned to the pocket.

b) the selected ticket is returned to the pocket.

a)

b)

The tickets can be selected in 120 or 216 ways.

8.Number of permutations without repetition with k=3 from x members is lower than number of permutations with repetition with k=3 from x members by 225. How many members are there?