QUESTION

(a) A bowl contains ten red balls and ten blue balls. A woman selects balls at random without looking at them.

i) How many balls must she select to be sure of having at least three balls of the same colour?

ii) How many balls must she select to be sure of having at least three blue balls?

(b) The English alphabet contains 21 consonants and 5 vowels. How many strings of six lowercase letters of the English alphabet contain

i) Exactly one vowel?

ii) Exactly two vowels?

iii) At least one vowel?

iv) At least two vowels?