Counting Principles - Pre Test

How many three-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?

Mathematical Equivalence

ON

Answer explanation

Explanation: The total number of choices for the hundreds place is 5 (excluding zero). For the tens place, after choosing one digit for the hundreds place, there are 4 remaining digits available. Similarly, for the units place, after choosing two digits for the hundreds and tens places, there remain 3 digits available. Therefore, the total number of ways is 5×4×3=60

In how many ways can the letters of the word "ALGEBRA" be arranged?

Mathematical Equivalence

OFF

Answer explanation

Explanation: The word "ALGEBRA" has 7 letters, but some letters are repeated. Therefore, the total number of ways to arrange them is 7! divided by the number of repetitions, which is 2! for the two A's. Hence, 7! : 2! = 2520

Calculate the number of ways of choosing 4 books from a shelf containing 8 different books.

Mathematical Equivalence

OFF

In how many ways can a president, vice-president, and treasurer be selected from a group of 10 students?

Mathematical Equivalence

ON

A committee of 5 students is to be formed from a group of 10 students. In how many ways can this committee be formed?

Mathematical Equivalence

ON

How many ways can 3 prizes be awarded among 8 contestants if each contestant can win at most one prize?

Mathematical Equivalence

ON

A standard deck of playing cards contains 52 cards. What is the probability of drawing a heart or a queen from the deck?

Mathematical Equivalence

OFF

In a group of 20 students, how many different pairs can be formed for a dance partnership?

Mathematical Equivalence

ON