Im stuck on questions can anyone help me ?
A)Which situation can be modeled by tossing a coin 3 times
choosing which one of sixteen teams will win a tournament?
B)picking one of six math teacher,
C)decide which English teacher of eight will win a trip to London
D)selecting a desk from 36 in a classroom
there are five floor plans , four exterior colors ,and an option of either a 2 or 3 car garage , how many choices are possible for one home
Of course, I can help you with that.
A) For this situation, you need to use the concept of permutation, where the order does matter. Tossing a coin 3 times can be modeled by using the concept of flipping a coin, where you have 2 possibilities (heads or tails) on each toss. Since there are 3 tosses, you multiply the number of possibilities by itself 3 times: 2 * 2 * 2 = 8 possibilities. Therefore, tossing a coin 3 times gives you 8 possible outcomes.
B) To find the number of choices possible for picking one of six math teachers, you need to use the concept of combinations. Since the order in which you pick the math teachers does not matter, you can use the concept of combination. The formula for combination is nCr, where n is the total number of options and r is the number of options you are choosing. In this case, you have 6 math teachers to choose from, and you need to pick one. So the formula becomes 6C1, which simplifies to 6. Therefore, there are 6 possible choices for one math teacher.
C) Similar to the previous situation, you also need to use the concept of combinations to find the number of choices possible for deciding which English teacher out of eight will win a trip to London. Again, the order does not matter. So the formula becomes 8C1, which simplifies to 8. Therefore, there are 8 possible choices for one English teacher.
D) For selecting a desk from 36 in a classroom, you can use the concept of combinations as well. Since the order does not matter, you need to calculate the total number of combinations. The formula for combination is nCr, where n is the total number of options and r is the number of options you are choosing. In this case, you have 36 desks to choose from, and you need to pick one. So the formula becomes 36C1, which simplifies to 36. Therefore, there are 36 possible choices for selecting a desk.
E) To calculate the number of choices possible for one home, you need to use the concept of multiplication. There are 5 choices for floor plans, 4 choices for exterior colors, and 2 choices for garage size (either a 2 or 3 car garage). To find the total number of choices, you need to multiply these options together: 5 * 4 * 2 = 40. Therefore, there are 40 possible choices for one home.