to arrange the top four finishers A new computer store offer

to arrange the top four finishers? A new computer store offers a special early-bird prize give-away for its grand opening. The first 12 customers to enter the store between 7 a.m. and 8 a.m. will receive gift certificates worth various dollar amounts. If 18 customers gather to enter the store between those hours, how many ways are there to arrange the twelve prize winners? 4. A state university issues five-digit student identification numbers to all of its students. Non the identification numbers contain the digit 0 and the digits cannot be repeated. How many ways are there to arrange five digits if only the numerals 1 through 9 are used? © K12 Inc.

Solution

(a) Out of 18 people first 12 will get gifts. As there is no mention of different gifts based on time of entry

Its a question of selction =18c12 = 18!/(12!6!) = 18564 ways this can happen

(b) 5 digit identifcation numbers without repitition of digits =

1st digit have 9 options

2nd digit have 8 options

3rd digit have 7 options

4th digit have 6 options

5th digit have 5 options

So total ways= 9*8*7*6*5 =15120