(a)You need to buy 8 pieces of fruit using apples, pears, oranges, and bananas.
ID: 3302844 • Letter: #
Question
(a)You need to buy 8 pieces of fruit using apples, pears, oranges, and bananas. How many ways of buying are there? (EX. you can buy 3 apples,1 pear,4 oranges and - bananas).
(b)How many ways are there to arrange the letters WATER in a circle, if we consider two arrangements to be the same if one can be gotten from the other after a rotation? (for example, suppose clockwise from the top we have ATRWE , then this is considered equivalent with the situation where clockwise from the top we have RWEAT)
Explanation / Answer
Solution:-
a) You need to buy 8 pieces of fruit using apples, pears, oranges, and bananas. How many ways of buying are there?
Let say we have 2 apples,3 pear, 2 oranges and 1 bananas
No. of ways we can buy them is 2*3*2*1 = 12 ways
Let say we have 1 apples, 1 pear, 5 oranges and 1 bananas
No. of ways we can buy them 1*1*5*1 = 5 ways
In the question it is not mentioned, whether we must include each fruit every time. Thus, we can follow the same concept to find the number of ways.
b) We can use the combination method to work this,
C(n,r) = n! / (r!(nr)!)
C (5,1) = 5! / 1!(5-1)! = 5
Therefore, there are 5 ways without repetition.
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