Answer Happy

Question 5 (a) You buy 10 cooldrinks. There are 5 types available. How many different selections are possible? (b) And if there is only 1 of type 2 left? (c) And if there is only 1 of types 1 and 2 teft? Question 6 (a) How many numbers with digits 1.2.3.4 of length 10 contain exactly sa 3's? (b) How many contain no 4's? Question 7 (a) What is the probability that boys and girls alternate in a random row arrangement of 3 boys and 3 girls? (b) What is the probability that a random arrangement of a.b.c.d has the letter b first? Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1-12 around a square, 3 numbers along each side of the square, that the numbers along at least one of the sides must add up to 20 or more (b) How many friends must you have to guarantee at least 5 of them will have birthdays in the same month. Use the extended pigeonhole principle Question 9 Let A = 12.3.4,6,9,12,18) and define a relation Ron A as follows Rhif and only if u and I have the same prime factors. (For example, 3R9 since both 3 and 9 have only the prime factor 3. But 6.89 since 6 has 2 and 3 as prime factors and 9 has only 3 as prime factor) (a) Draw the directed graph of R. (b) Give the in/out degrees of 3 and 18. (c) Give the domain and range of R.