Question

Learning Task 3: Be Wise to Decide

Maria’s sister from Los Baños went to San Pablo City to visit her because it’s
almost a year that they did not see each other due to COVID-19 pandemic.
They were so much excited to embrace one another. To enjoy the time with
each other, they decided to go to San Pablo Shopping Mall and Market to stroll
and buy something. They brought with them four eco bags: green, blue, red,
and yellow.
1. They bought five kinds of fruits such as apples, grapes, bananas,
pomelo, and oranges. In how many ways can they arrange three fruits
on a green bag if no repetition will be made and order is not
important?
2. They bought three flat shoes of different colors, red, brown and cream,
upstairs of the shopping mall. They decided to put them inside the red
eco bag, but it can only contain two pairs of shoes. In how many ways
can they arrange the boxes considering which is at the top and which
is at the bottom.
3. They planned to make a chicken vegetable salad; thus, they bought
carrots, potatoes, lettuce, cabbage, pineapple, quail eggs, and chicken as the main ingredients. In how many ways can they put the
four ingredients at a time?​

Answer 1

Step-by-step explanation:

Learning Task 3: Be Wise to Decide

Maria’s sister from Los Baños went to San Pablo City to visit her because it’s

almost a year that they did not see each other due to COVID-19 pandemic.

They were so much excited to embrace one another. To enjoy the time with

each other, they decided to go to San Pablo Shopping Mall and Market to stroll

and buy something. They brought with them four eco bags: green, blue, red,

and yellow.

1. They bought five kinds of fruits such as apples, grapes, bananas,

pomelo, and oranges. In how many ways can they arrange three fruits

on a green bag if no repetition will be made and order is not

important?

2. They bought three flat shoes of different colors, red, brown and cream,

upstairs of the shopping mall. They decided to put them inside the red

eco bag, but it can only contain two pairs of shoes. In how many ways

can they arrange the boxes considering which is at the top and which

is at the bottom.

3. They planned to make a chicken vegetable salad; thus, they bought

carrots, potatoes, lettuce, cabbage, pineapple, quail eggs, and chicken as the main ingredients. In how many ways can they put the

four ingredients at a time?

Answer 2

Answer:

1) 10 ways

2) 6 days

3) 35 ways

Step-by-step explanation:

Concept

• The act of organizing items or numbers in order is known as Permutation. Combinations are a method of picking things or numbers from a set of objects or a collection without regard to their order.
• The formula for permutations is: nPr = n!/(n-r)!
• The formula for combinations is: nCr = n!/[r! (n-r)!
• Probability is the state of being able to do something. It's a branch of mathematics that deals with the randomness of events. From zero to one, the value is stated. In mathematics, the concept of probability was established to predict the likelihood of occurrences occurring. Probability refers to the likelihood of something occurring. This is the fundamental probability theory, which is also employed in the probability distribution, where you will learn about the possible results of a random experiment. We must first know the entire number of possible outcomes in order to calculate the probability of a particular event occurring.

Find

Solution of 1, 2 and 3

Solution

1) $5C^{3}$=$\frac{5!}{3!(5-3)!}$

       =$\frac{5!}{(3,2,1)(2)!}$

      =$\frac{60}{6}$

     =10 ways

2) $3P^{2} =\frac{3!}{(3-2)!}$

          =$\frac{3!}{1!}$

         =6 days

3) $7C^{4} =\frac{7!}{4!(7-4)!}$

          =$\frac{210}{6}$

         $=35 ways$

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