INFO2100 - Mathematics and Statistics for IT

Exercise Set 1 January 26, 2015

1. (a) In how many ways can the letters the word MATHEMATICS be arranged?

(b) If the letter of the word MATHEMATICS are arranged in a line at random, what isthe probability that the arrangement begins with MM?

2. How many different codes can be formed if each is to contain the four letters INFO followedby the four digits 2100?

3. The digits 0, 1, 2, 3, and 4 are to be used in a four digit password. How many different passwordsare possible

(a) if repetitions are allowed?

(b) if repetitions are not allowed?

4. An urn contains five balls whose colours are red, blue, black, brown and white. A ball isselected, its colour is noted, and replaced. Then a second ball is selected, and its colour isnoted.

(a) How many different colour schemes are possible?

(b) If the first ball is not replaced, how many different colour schemes are possible?

5. How many ways can 5 books be arranged on a shelf if they can be selected from 10 books?

6. Two letters are chosen at random from the word THEORY .

(a) Find the probability that all two letters are consonants.

(b) Find the probability that all two letters are vowels.

END OF EXERCISE SET 1

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