In 1713 , the work of J. Bernoulli was published "The Art of Assumptions", in which combinatorial facts known by that time were presented with sufficient completeness. "The Art of Assumptions" was not completed by the author and appeared after his death. The essay consisted of 4 parts, the second part was devoted to combinatorics, which contains a formula for the number of permutations of n elements.
Example
In how many ways can 8 people line up at the box office?
After one person took the first place, there are 7 places left and 7 people who can be placed on them, i.e. ways to take second place - 7. Similarly for the third, fourth, etc. places.
Using the principle of multiplication, we get the product. Such a product is designated as 8! (read 8 factorial) and is called a permutation of P 8.
1) In how many ways can four different books be placed side by side on a shelf?
Answer: 24 ways Solution.
In the first place, you can put one of the four books, in the second - any of the three, in the third - any of the two and in the fourth - the last remaining book. Applying successively the product rule, we get Р(4) = 4х3х2х1=24.
check yourself
2) In how many ways can 10 different postcards be put into 10 existing envelopes (one postcard per envelope)?
SOLUTION
check yourself
2) In how many ways can 10 different postcards be put into 10 existing envelopes (one postcard per envelope)?
