Three digit numbers are formed from 5 cards labelled 1,2,3,4 and 5.
A) how many different 3-digit numbers can be formed?
Choose the first digit any of the 5 ways.
Choose the second digit any of the 4 remaining unchosen digits.
Choose the third digit any of the 3 remaining unchosen digits.
Answer: 5P3 = 5∙4∙3 = 60
B) if one of these numbers is selected at random what is the probability
that it is odd?
Choose the third digit any of 3 ways (1,3 or 5)
Choose the first digit any of the 4 remaining unchosen digits.
Choose the third digit any of the 3 remaining unchosen digits.
Number of different odd 3-digit numbers = 3∙4∙3 = 36 ways.
Probability of odd 3-digit number = 36/60 = 3/5
C) how many of these 3-digit numbers are even?
Easy way (using B): 1 - 3/5 = 5/5 - 3/5 = 2/5
Or From scratch (without using B):
Choose the third digit any of 2 ways (2 or 4)
Choose the first digit any of the 4 remaining unchosen digits.
Choose the third digit any of the 3 remaining unchosen digits.
Number of different even 3-digit numbers = 2∙4∙3 = 24 ways.
Probability of even 3-digit number = 24/60 = 2/5
D) what is the probability of randomly selecting a 3- digit number less than
500 with its digits arranged in descending order
Consider the 4-digit number with its digits arranged in descending
order: 4321
If we remove any one of those 4 digits from 4321 the remaining 3 will form a
number less than 500 with digits in descending order. That's 4 digits
choose 1 to remove, or 4C1 = 4 ways.
Probability of a 3-digit number less than 500 with its digits arranged in
descending order = 4/60 = 1/15.
Edwin
