You are taking a multiple-choice test that has 7 questions. Each of the questions has 5 choices, with one correct choice per question.

a)If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?

b) in a test of a gender-selection method, 14 babies are born and 10 of them are girls,

i) Find the number of different possible sequences of genders that are possible when 14 babies are box.
ii) How many ways can 10 girls and 4 boys be arranged in a sequence?

a) 78125 b) i) 87178291200   ii) 174182400

Step-by-step explanation:

a) number of ways in which seven questions can be answered= 5⁷= 78125

b)  i) When all fourteen baibes are arranged without gender consideration that is 14 babies are box

14!= 87178291200

 ii) When 10 girls and 4 boys are arrnged such that girls are to be together and boys are to be together

2×10! × 4 ! = 174182400

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: