1 In the land of Noom, all nouns are 4-letter words with consonants at the beginning and end and a repeated vowel (a, e, i, o, or u) in the middle. How many such words are possible?

2 How many positive three-digit integers are there in which the sum of its three digits is odd?

3.What is the least positive integer with exactly 10 factors?

sudsw12 Apr 13, 2019

#1**+1 **

1 In the land of Noom, all nouns are 4-letter words with consonants at the beginning and end and a repeated vowel (a, e, i, o, or u) in the middle. How many such words are possible?

Assuming that the first and last consonants can be repeated....we have 21choices for each [ 21 consonants]

So....the number of possible nouns =

21 * 5 * 21 = 2205 nouns

However.....if the two consonants must be different, then only

21 * 5 * 20 = 2100 nouns

CPhill Apr 13, 2019

#2**+1 **

3.What is the least positive integer with exactly 10 factors?

The integer is

2^4 * 3 = 48

CPhill Apr 13, 2019

#3**+1 **

2 How many positive three-digit integers are there in which the sum of its three digits is odd?

An odd sum will occur if we have

odd even even even odd even even even odd

( 5 * 5 * 5 ) (4) * (5) * (5) (4) * (5) * (5)

125 + 100 + 100

325

OR

odd odd odd

5 * 5 * 5

125

So...there will be 325 + 125 = 450 three-digit integers

CPhill Apr 13, 2019