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# permutations

0
177
5

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?

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   Apr 13, 2019
#4
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Hi CPhill,

Where in the problem does it state that the two consonants have to be different? Is it implied in a part of the problem?

sudsw12  Apr 13, 2019
#5
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It doesn't say....I showed both cases

Which is correct.....I don't know.....   CPhill  Apr 13, 2019
#2
+1

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

The integer  is

2^4 * 3  =    48   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   Apr 13, 2019