All GMAT Math Resources
Example Questions
Example Question #2 : Counting Methods
Twelve students are running for student council; each student will vote for four. Mick wants to vote for his sister Janine. How many ways can he cast his ballot so as to include Janine among his choices?
Since one of Mick's choices is already decided, he will choose three people from a set of eleven without regard to order. This is a combination of three from a set of eleven; the number of such combinations is:
Example Question #1 : Understanding Counting Methods
Twelve students are running for student council; each student will vote for five. Claude does not want to vote for Gary or Mitch, neither of whom he likes. How many ways can Claude fill in the ballot so that he does not vote for Gary?
Claude will choose five people from a set of ten - twelve minus the two he dislikes - without regard to order. This is a combination of five from a set of ten; the number of such combinations is:
Example Question #331 : Arithmetic
The Department of Motor Vehicles wants to make all of the state's license numbers conform to two rules:
Rule 1: The license number must comprise three letters followed by four numerals.
Rule 2: Numerals can be repeated, but letters cannot.
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
Three different letters are selected from a group of 26, order being important - this is a permutation of three elements out of twenty-six. These permutations number .
There are then four numerals, each chosen from a set of ten. Since repeats are allowed, the number of ways this can be done is
By the multiplication principle, there are
possible license plates.
Example Question #12 : Counting Methods
The Department of Motor Vehicles wants to make all of the state's license numbers conform to three rules:
Rule 1: The license number must comprise three letters (A-Z), followed by three numerals (0-9), followed by a letter.
Rule 2: Repeats are allowed.
Rule 3: None of the letters can be an "O" or an "I".
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
There are 24 ways to choose an allowed letter (since two of the 26 are excluded) and 10 ways to choose an allowed digit. Since repeats are allowed, and four letters and three digits will be chosen, there will be
possible license plate numbers.
Example Question #1882 : Problem Solving Questions
The Department of Motor Vehicles wants to make all of the state's license numbers conform to four rules:
Rule 1: The license number must comprise two letters, followed by three digits, followed by two letters.
Rule 2: The letters "I" and "O" may not be used.
Rule 3: The digits "0" and "1" may not be used.
Rule 4: Repeats are allowed.
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
Each of the four letters can be selected twenty-four ways, since two letters are forbidden and since repeats are allowed. Similarly, each of the three digits can be selected eight ways for the same reason.
By the multiplication principle, the number of possible license plate numbers is
Example Question #1883 : Problem Solving Questions
The Department of Motor Vehicles wants to make all of the state's license numbers conform to three rules:
Rule 1: Each license number must comprise six characters, each of which must be a letter or a digit.
Rule 2: No license number can comprise six letters or six digits.
Rule 3: Repeats are allowed.
Which of the following expressions is equal to the number of possible license numbers that would conform to this rule?
Each character of the licence plate number can be chosen from a set of 36 (26 letters plus 10 digits), and any character can be chosen multiple times. By the multiplication principle, this would allow different licence numbers. But licence numbers that comprise only letters and those that comprise only digits are disallowed, so by similar math, this reduces the possibilities by and , respectively.
Therefore, there are allowed licence plate numbers.
Example Question #332 : Arithmetic
Jessica went shopping and bought herself shirts, skirts, and pairs of shoes. How many outfits can Jessica possibly create from what she just bought?
She has 4 choices for the shirt, 2 choices for the skirt per shirt chosen, and 3 choices for the pair of shoes per combination of shirt and skirt:
4 x 2 x 3 = 24 possible outfits
Example Question #333 : Arithmetic
Fred shuffles a deck of 52 cards. He then draws 1 card and keeps it. Then he draws a 2nd card. Then he puts it back into the deck and shuffles again. Fred then draws a 3rd card and keeps it
What's the probability that the 2nd and 3rd cards are the same?
None of the other answers
Just before Fred draws the 2nd card, there are 51 cards in the deck, because he already took the 1st card out.
Then once he puts the 2nd card back in, and shuffles, there are still 51 cards in the deck; he did not put the 1st card back in.
So Fred has a 1 in 51 chance of drawing the same card again.
Example Question #334 : Arithmetic
Simplify the following expression
None of the other answers
Factorial numbers such as are evaluated as follows;
So to evaluate the expression
(Start)
(Expand the factorials)
(Cancel the common factors)
(Simplify)
Example Question #14 : Understanding Counting Methods
In how many ways can the letters , , and be arranged to form a four-letter combination?
This combination problem asks us the number of ways to arrange four letters, including two that are the same. Four different letters can be arranged in different ways, but since we have two of the same letter, , we have to divide by . In any combination problem, if we have a total of letters, then for every number of the same letters, we have .