# Mates y TIC - Maths and ICT

## Combinatorics

Posted by ricardogm on May 28th, 2019

Hi

1. Two possibilities for today:

a) Use this hour for the project.

b) Solve combinatorics problems, below.

Here you are:

Permutations and combinations

Same thing in spanish

Another

And some examples.

And a calculator

Factorial calculator.

Some simple problems to practice:

6. How many ways can you arrange the letters from the word CODES?
7. At Scrabble you have the letters XZJYPVK. How many 3 letter arrangements can be
8. At travelling sales man must visit 15 towns. In how many different ways can he plan his
journey?
9. How many numbers between 100 and 1000 use only odd digits, no digit being repeated?
10. In Mastermind a code is picked using 4 out of 6 colours. How many codes are possible, if
no colour can be used twice?
11. There are 14 horses in a race. In how many ways can the first 3 places be filled?
12. A class contains 25 pupils. In how many ways can prizes be awarded in Latin, French and
Mathematics, if no pupil can win more than one prize?
13. In how many ways can eight books be arranged along a shelf?
14. At Scrabble the letters QWYPKGDZXBM are left in the bag. In how many ways can you
draw out four of them?
15. You are given 12 points on a plane, no three of them being in a straight line. How many
triangles can be drawn using the points as vertices?
16.You are given 9 points on a circle. How many chords do they form?
17. You have 10 blue flowers are 5 b red flowers. In how many ways can they be planted in a
row, if we do not distinguish between flowers of the same colour?
18. The travelling salesman of Question 8 decides to visit only 5 towns. In how many ways
can his selection be made? How many possible journeys does he have now?
19. In Bridge each player receives 13 out of the 52 cards. How many possible Bridge hands
are there?
20. A coin is tossed 10 times, and heads comes up 4 times. In how many ways can this have
happened?
21. You win a tennis set 6-4. How many ways can this have happened?

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