A box contains 3 different varieties of apples. What is the smallest number of apples that must be taken to be sure of getting at least 2 of one kind? How about at least 3 of one kind? How about at least 10 of a kind? How about at least "n" of a kind?
2007-04-20 05:50:52 · 3 answers · asked by Anonymous in Education & Reference ➔ Homework Help
You always pick one more than the amount of varieties to ensure 2 of a kind.
If there's 3 varieties you pick 4 apples, 5 varieties you pick 6, etc. etc.
2007-04-20 05:59:19 · answer #1 · answered by Anonymous · 0⤊ 1⤋
If there are three different types you would need to take four out to guarantee two of a kind. To get three of a kind you would need to draw seven. For ten of a kind you would need to draw twenty eight. The formula is simple. Whatever number you need draw twice the amount of one less than needed plus the number you need.
IE
If it was seven then 2 x 6 = 12
12 + 7 = 19
So draw 19 to guarantee 7 of one kind. You could, of course draw seven from the first seven drawn but this would be unlikely.
2007-04-20 12:58:53 · answer #2 · answered by quatt47 7 · 0⤊ 0⤋
You would need 4 to get 2 of one kind. To get 3 of one kind, you need to grab 7. To get 10, you need to grab 28.
The formula is n*3-2.
For example 20, you need to grab 20*3-2=60-2=58.
2007-04-20 13:14:20 · answer #3 · answered by JO 3 · 0⤊ 0⤋