How many words may be created with three consonants and two vowels from a set of seven consonants and four vowels?
A. 210
B. 1050
C. 25200
D. 21400
Answer:C
How many words may be created with three consonants and two vowels from a set of seven consonants and four vowels?
A. 210 B. 1050 C. 25200 D. 21400
Explanation: There are three consonants out of seven to choose from, and (2 vowels out of 4).7 x 6 x 5/3 x 2 x 1 2 x 1 x 4 x 3/2 x 1 = (7C3 x 4C2) = 7 x 6 x 5/3 x 2 x 1 2 x 1 x 4 x 3/2 x 1equals 210,There are 210 groups, each with three consonants and two vowels.There are five letters in each group.The number of different ways to arrange five letters is 5! = 5 x 4 x 3 x 2 x 1 = 120.Number of methods required = (210 x 120) = 25200.