Question

Jimmy found five numbered cards, 1, 2, 3, 4, and 5 under his brother's bed. In how many ways can he arrange the cards to form a five-digit number?

Answer 1

120 ways

Explanation:

Given.

Cards numbered 1 - 5

Required

Number of arrangements

First, it should be noted that there's no way Jimmy can repeat cards because the each card contains distinct numbers.

Having said that;

Number of cards = 5

Required digit = 5-digit

This question will be solved using permutation formula.

nPr = n!/(n - r)!

Where

n = number of cards = 5

r = number of digits = 5

So,

nPr = n!/(n - r)! becomes

5P5 = 5!/(5 - 5)!

5P5 = 5!/0!

5P5 = 5!/1

5P5 = 5!

5P5 = 5 * 4 * 3 * 2 * 1

5P5 = 120 ways.

Hence, number of possible arrangements Jimmy can arrange the card is 120 ways.