In how many ways can the letters in \"HOUSE\" be arranged if there are no restri
ID: 3004539 • Letter: I
Question
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} areExplanation / Answer
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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