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1 year ago

How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?

1 answer:

3 0

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

According to the given question.

The total number of elements, n = 3

The number of elements to be selected at a time when repetition is allowed, r = 5

Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is $n^{r}$ .

Therefore,

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed

= $3^{5}$

= 243

Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

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Without having to raise funds externally sales could increase by $84,507.04.

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The amount of sales increase that the company can achieve without having to raise funds externally is calculated by multiplying the current year sales with the self-supporting growth rate.

Current Year Sales = $4,000,000

Profit Margin = 3.00%

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Total Spontaneous Liabilities is, $200,000 + $100,000=$300,000

Last Year Total Assets = $3,200,000

Therefore, the Self-supporting Growth Rate=Addition to Retained Earnings÷[Total Assets–Total Spontaneous Liabilities-Addition to Retained Earnings]

= [Last year sales×Profit Margin×(1-Dividend Payout Ratio)]÷[Total Assets-Total Spontaneous Liabilities-Addition to Retained Earnings]

= [$4,000,000×0.03×(1–0.50)]÷[$3,200,000-$300,000–{[$4,000,000×0.04×(1–0.050)}]

= $60,000÷[$3,200,000-$300,000-$60,000]

= $80,000÷$2,840,000

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Therefore, the increase in sales that the company can achieve without having to raise funds externally = Last Year Sales×Self-supporting Growth Rate

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