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3 years ago

Solve for x. X+ 2 1/5=5 3/5

Mathematics

2 answers:

Alexxandr [17]3 years ago

3 0

Answer:

x=17/5

Step-by-step explanation:

2 1/5=11/5

5 3/5=28/5

------------------

x+11/5=28/5

x=28/5-11/5

x=17/5

forsale [732]3 years ago

3 0

x+ (2 + 1/5)=(5 + 3/5)

5x = 17

x = 17

5 = 3.4

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In total, $120$ permutations of three items can be selected from a group of six distinct elements.

In particular, there are $6$ ways to order three distinct items.

$\begin{aligned}\rm B-D-F \\ \rm B-F-D \\ \rm D-B-F \\ \rm D-F-B \\ \rm F-B-D \\ \rm F-D-B\end{aligned}$ .

Step-by-step explanation:

The formula $\displaystyle P(n,\, r) = \frac{n!}{(n - r)!} = n \, (n - 1) \cdots (n - r + 1)$ gives the number of ways to select and order $r$ items from a group of $n$ distinct elements.

To select and order three items from a group six distinct elements, let $n = 6$ and $r = 3$ . Apply the formula:

$\begin{aligned} P(6,\, 3) &= \frac{6!}{(6 - 3)!} = \frac{6!}{3!} \\ &= \frac{6 \times 5 \times 4 \times 3\times 2 \times 1}{3 \times 2 \times 1} \\ &= 6 \times 5 \times 4 = 120 \end{aligned}$ .

In other words, there are $120$ unique ways to select and order three items (select a permutation of three items) from a group of six distinct elements.

Consider: what's the number of ways to order three distinct items? That's the same as asking: how many ways are there to select and order three items from a group of three distinct elements? Let $n =3$ and $r = 3$ . Apply the formula for permutation:

$\begin{aligned} P(3,\, 3) &= \frac{3!}{(3 - 3)!} = \frac{3!}{0!} && \left(\text{$0! = 1$ by convention.}\right) \\ &= 3! = 3 \times 2\times 1 \\ &= 6\end{aligned}$ .

To find the permutations, start by selecting one element as the first of the list. A tree diagram might be helpful. Refer to the attachment for an example.