QuestionNovember 22, 2024 at 10:28 AM A sports store has 7 female clerks and 9 male clerks. Each day Monday - Saturday next week the owner will select one out of all of these clerks (so repetitions are possible) to be the greeter. In how many overall outcomes would both women and men be selected?
Studdy Solution
STEP 1
1. The store has 7 female clerks and 9 male clerks.
2. The selection of a greeter occurs once per day from Monday to Saturday.
3. Repetitions of selections are allowed.
4. We are interested in the number of outcomes where both women and men are selected at least once during the week.
STEP 2
1. Calculate the total number of possible outcomes for the week.
2. Calculate the number of outcomes where only women are selected.
3. Calculate the number of outcomes where only men are selected.
4. Use complementary counting to find the number of outcomes where both women and men are selected.
STEP 3
Calculate the total number of possible outcomes for the week.
Each day, a greeter can be selected from a total of clerks.
Since there are 6 days, the total number of outcomes is:
STEP 4
Calculate the number of outcomes where only women are selected.
If only women are selected, each day a greeter is chosen from 7 female clerks.
The number of outcomes where only women are selected is:
STEP 5
Calculate the number of outcomes where only men are selected.
If only men are selected, each day a greeter is chosen from 9 male clerks.
The number of outcomes where only men are selected is:
STEP 6
Use complementary counting to find the number of outcomes where both women and men are selected.
The number of outcomes where both women and men are selected is the total number of outcomes minus the outcomes where only women or only men are selected:
The number of outcomes where both women and men are selected is:
Was this helpful?
