Question

1.How many positive three-digit integers can be made from the digits {3,4,5,6,7} if digits may be repeated? 5x4x3=60
2.In how many ways can all of the letters of the word HEXAGON be arranged if the arrangement must start with a consonant and end in a vowel? 4x3x1x2x3x4x5=1440
3.How many positive integers between 3000 and 4000 can be made with the digits {3,4,6.9} if repetition of digits is allowed? 3x1x2x3
4.How many 7-digit phone numbers can be made if the first three digits can only be 3's or 4's but there are no restrictions on the last four digits?(Don't know this one)

Answer 1

#1. 5 choices for each digit.
So, 5^4

#2. correct

#3. 1 * 4^3

#4. 2^3 * 10^4

when repetitions are allowed, you get more choices...