For each day of the 5-day working week Tom can choose any
one of 6 newspapers to read at the lunchtime.
(i) How many different choices are possible in a week?
(ii) If Tom wants to read a different title each day, then how
many different choices are possible in a week?
To determine the number of different choices Tom has in a week, we need to consider each day independently and then multiply the choices for each day together.
(i) To find the number of different choices without any restrictions, we can simply calculate the total number of choices for each day and multiply them together.
Since Tom can choose any one of the 6 newspapers for each day of the week, the total number of choices for each day is 6.
Therefore, the total number of different choices possible in a week for Tom is 6 multiplied by 6, for each day of the week:
6 x 6 = 36
So, there are 36 different choices possible in a week for Tom.
(ii) If Tom wants to read a different title each day, the choices for each day will be limited. To calculate the number of different choices in this case, we can use the concept of permutations.
On the first day, Tom can choose any newspaper out of the 6 available titles, giving us 6 choices.
On the second day, Tom cannot choose the same newspaper as the previous day, so he has 5 options left.
Proceeding in the same manner, for the third day, Tom has 4 choices, for the fourth day, Tom has 3 choices, and for the fifth day, Tom has 2 choices.
Using the principle of multiplication, we can determine the total number of different choices by multiplying the choices for each day together:
6 x 5 x 4 x 3 x 2 = 720
Therefore, if Tom wants to read a different title each day, there are 720 different choices possible in a week.