Susanna owns 10 shops and 5 restaurants. She is going to visit three of her businesses and writes her list in order.
The order will be:
Shop, restaurant, shop
OR
Restaurant, shop, restaurant.
How many different lists can Bethany write?
Thank you.
SRS: 10*5*9
RSR: 5*10*4
To find out how many different lists Susanna can write, we need to consider the number of ways she can choose the type of business (shop or restaurant) for each visit, as well as the order of these visits.
We have 10 shops and 5 restaurants, so the first visit can be either a shop or a restaurant, giving us 15 options. The second visit will then have 14 options (as we have already visited one business), and the third visit will have 13 options.
Since the order of the visits matters, we need to consider the permutations of these options. The number of permutations of 15 options taken 3 at a time is given by the formula:
nPr = n! / (n - r)!
Where n is the total number of options (15) and r is the number of choices we are making (3).
So, the number of different lists Susanna can write is:
nPr = 15! / (15 - 3)!
= 15! / 12!
= (15 * 14 * 13) / (3 * 2 * 1)
= 455
Therefore, Susanna can write 455 different lists.