In how many ways can the letters in HOUSE be arranged if the

In how many ways can the letters in \"HOUSE\" be arranged if there are no restrictions? the vowels must be together? no two vowels are adjacent? no two consonants are adjacent? A card is drawn randomly from a deck of cards and then a second card is drawn. How many different pairs are there if the order in which cards are drawn is considered important? (i.e., drawing K, then 7 is different than 7, then K) How many different pairs are there if the order in which cards are drawn is not considered important? How many integers in {1,2,3,...,300} are

Solution

Post one moer question to get the remaining answers

Q3)

a) In how many ways HOUSE if there are no restriction

Number of ways = 5! = 120 ways

b) vowels must be together

Combine two vowels (O,E) and three HSE

Hence the number of ways = 4!(four letters) * 2!(rearranging O and E)

=> 24 * 2 = 48 ways

c) no towels are adjacent

Number of ways = 120 - 48 = 72 ways

d) no two consonants are together

Number of ways = 72 ways