Combination
Formula for combination
n!/r!(n-r)!
Permutation formula
nPr=n!/(n-r)!
Outfits you can make with 3 shirts, 5 shoes, and 6 pairs of pants. (all clothing and shoes are distinct)
90
P(selecting 6 in a 10 face dice, numbered 1-10)
1/10
You're outside a room with 3 light switches. One controls a bulb inside the room. You can flip switches as much as you want, but you can only enter the room once. How do you figure out which switch controls the bulb?
Turn on switch 1 for a few minutes, then turn it off. Turn on switch 2, then enter the room.
· Bulb on → switch 2 · Bulb off but warm → switch 1 · Bulb off and cold → switch 3
6C2 value
10
Ways to arrange 6 people in a line
6!=720
A license plate has 2 letters followed by 3 digits. (strictly in this order) Assuming letters and numbers can repeat, this is the total number of possible plates.
262 x 103
P(sum of 2 values rolled in a regular 6 face dice are even)
1/2
A hotel has infinitely many rooms, all occupied. A new guest arrives. Can the hotel fit them in?
Yes. Move the guest in room 1 to room 2, room 2 to room 3, room 3 to room 4, etc. Now room 1 is free.
Ways to line A,B,J,M1,M2 in a line, when M1 and M2 insists to be standing together.
4!x2!=48
Answer for 6P3
6x5x4=120
Ways of 4 character password with 1 digit, 1 letter, 1 digit, 1 letter (strictly followed by this pattern)with no repeating allowed.
10x26x9x25=58,500
P(drawing red marble from a bag with 5 red marbles and 3 blue marbles)
5/8
Someone have 6 apples. You take away 5. How many apples do you have?
5
Ways to seat 6 people in a circle
5!=120
Ways to arrange letters in BANANA
6!/(2!x3!)=60
Ways of topping on pizzas with 7 meats, 6 cheese, 10 vegetables, and 24 other toppings.
7x6x10x24=10,080
P(Getting at least one head when flipping 2 fair coins)
3/4
Real roots for x2+46x+168
-4, -42
Ways to divide 6 people into two indistinct groups of 3
10
The number of ways gold, silver, and bronze medal can be awarded in a race of 8 runners
8P3=8x7x6=336
A student has 4 different math books, 3 different science books, and 2 different history books. This is the number of ways to arrange them on a shelf if all books of the same subject must stay together.
6x24x6x2=1,728
P(Selecting 2 red marbles in a bag containing 4 red marbles and 6 blue marbles without replacement)
2/15
Write a recursive formula for this geometric sequence: 1,0,0,0,0,0....
You can't write a recursive formula for this. 0/1 isn't the same as 0/0.