IQ TEST: Math, Probability, Permutations, Repetitions, Ordered Combinations, Exclusive events, Number of digits

1. If there are 10 people in a room and they would make handshakes with each one in the room, how many unique handshakes would be made?

find:

H = number of unique handshakes

solution:

n = number of people = 10

H = (n - 1) + (n - 2) + (n - 3) .....until LAST ADDEND is 1

first term = PEOPLE - 1


H = 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

H = 45


if there are only 5 people in the room

H = 4 + 3 + 2 + 1

H = 10


2. If a dice and a coin are tossed, what is the probability that you will get a 4 on the dice and heads on the coin?

solution:

P = Pdice * Pcoin

P = 1/6 * 1/2

P = 1/12


3. A circular spinner is marked W, X, Y, Z. what is the probability of NOT getting an X if spinned thrice?

solution:

if spinned once ---> P1 = 3/4

if spinned twice ---> P2 = 3/4 * 3/4 = 9/16

if spinned thrice ---> P1 = 3/4 * 3/4 * 3/4 = 27/64


4. There are 5 choices each question. What is the probability of correctly guessing 3 questions?

solution:

P = 1/5 * 1/5 * 1/5

P = 1/125


5. If you have 5 pants and 8 shirts, how many ways can you wear them?

solution:

W = 5 * 8

W = 40


6. In a restaurant, there are 3 choices of soup, 5 choices of entrees, and 2 choices of desert. How many ways can you order them if each order consists of one soup, one entree, and one desert?

solution:

W = 3 * 5 * 2

w = 30


7. If 4 warriors line up so that the order matters, how many ordered combinations (permutations) are possible?

P = 4 * 3 * 2 * 1

P = 24


8. If you count from 1 to 100, How many zeroes are there? How many sevens are there?

solution:

let

Zt = total number of 0's

St = total number of 7's


1 to 10 : z = 1, s = 1

11 to 20: z = 1, s = 1

21 to 30: z = 1, s = 1

31 to 40: z = 1, s = 1

41 to 50: z = 1, s = 1

51 to 60: z = 1, s = 1

61 to 70: z = 1, s = 2 (67, 70)

71 to 80: z = 1, s = 10 ( 71, 72, 73, 74, 75, 76, 77, 78, 79 ---> there are two 7's on 77 )

81 to 90: z = 1, s = 1

91 to 100: z = 2, s = 1 ( 100 ---> two zeroes on 100 )


Zt = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 = 11

St = 1 + 1 + 1 + 1 + 1 + 1 + 2 + 10 + 1 + 1 = 20