At a store, customers are randomly selected to participate in a survey. on friday, there were 500 customers at the store. out of all those people, 90 were selected to participate in the survey. on saturday, the store manager expects 700 customers in the store. if the probability of being selected to participate in the survey on saturday is the same as it was on friday, how many customers will be selected to participate in the survey on on saturday?

Divide the number of people selected by the total number of people.

90/500 = .18

This means that 18% of the customers were selected for the survey.

If the probability is the same on Saturday, then we can multiply the expected customers by our .18

700 x .18 = 126

126 should be selected for the survey on Saturday.

a)  6.402373706 × 10¹⁵

b) 1.609445376 × 10¹²

c) 7.966754611 × 10¹⁴

Step-by-step explanation:

a) Since they are 11 men and 8 women to be seated in a circle  and they can be arranged in any manner.

Therefore the total number of men and women = 11 men + 8 women = 19 people.

Since they are to be seated in a circle, the number of ways this can happen = (19 - 1)! = 18! = 6.402373706 × 10¹⁵

b) 11 men and 8 women in a row if the men all sit together and the women all sit together

First, the women are arranged in one group. 8 women can be seated in 8! ways.

The 11 men can be seated in the remaining 11 places in 11! ways

Therefore the number of arrangements = (11! × 8!) arrangements

                                                                  = 1.609445376 × 10¹²

c) If no 2 women sit together, that means between two men, there is at most 1 woman.

Firstly, we consider the position of the men. The number of ways 11 men can be arranged in a row =

Now as no two women stand next to each other,we can imagine the situation as:

*M*M*M*M*M*M*M*M*M*M*M*

To find how many ways we can arrange 8 women in the 12 possible places (as shown above) =

Using product rule, the number of arrangements = 39916800 × 19958400 = 7.966754611 × 10¹⁴