Counting - Day 1
1) How many ways are there to roll a 2 on a six-sided die?
2) How many ways are there to choose a queen from a standard deck of playing cards?
3) How many ways are there to arrange the letters A, B, C ?
4) … roll an odd number on a six-sided die?
5) … arrange the letters B, E, A, T ?
6) … roll a total of 7 on a pair of six-sided dice?
7) … arrange the (original) books of the Harry Potter series?
8) … create a 5-character computer password consisting only of (lowercase) letters?
9) … create a 5-character computer password consisting of two numbers followed by 3 letters?
Answers
1) 1
2) queen of clubs or queen of spades or queen of hearts or queen of diamonds = 4 ways
3) A _ _ A _ _ B _ _ B _ _ C _ _ C _ _ = 6 ways
choose A or B or C and choose from this or that of the and third spot is leftover letter
for first spot two leftover letters for second spot
(3 choices) * (2 choices) * (1 choice)
4) 1 or 3 or 5 = 3 ways
5) Like #3 above, you have 4 choices and then 3 choices and then 2 choices and then 1 choice = 4*3*2*1 = 24 ways
6) 1+6 or 2+5 or 3+4 or 4+3 or 5+2 or 6+1 = 6 ways
7) There are 7 books in the series. Don’t count those other money grab add-ons. It’s like #3 above.
7 choices and then 6 choices and then 5 choices and then … = 7654321 = 5040 ways
8) 26*26*26*26*26 = 11,881,376 ways
9) 10*10*26*26*26 = 1,757,600 ways