If a mother has three bananas, two pears, and two oranges, in how many different ways can she give the fruit to her daughter in one week, one piece of fruit per day?
dont knw :/
To determine the number of different ways the mother can give the fruit to her daughter in one week, we can use the concept of permutations. Since there are 3 bananas, 2 pears, and 2 oranges, we need to calculate the number of permutations for these fruits.
First, let's calculate the total number of fruits the mother has:
3 bananas + 2 pears + 2 oranges = 7 fruits
Now, let's determine the number of ways the mother can give the fruits to her daughter in one week, one piece of fruit per day. We'll calculate using the formula for permutations:
nPr = n! / (n-r)!
Where n is the total number of objects (in this case, fruits) and r is the number of objects selected each time (in this case, 1 fruit per day for 7 days). The exclamation mark (!) represents the factorial operation, which means multiplying all positive integers from 1 to the given number.
Substituting the values into the formula:
7P7 = 7! / (7-7)!
= 7! / 0!
= 7! / 1
= 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
Therefore, the mother can give the fruit to her daughter in 5040 different ways in one week, one piece of fruit per day.