Lamia has the letter cards A, Z, D, Y, and E in a bag. If she selects a permutation of the cards at random, what is the probability that she will spell the word "ZAYED”?

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Step-by-step explanation:

Note that all five letters here are distinct (i.e., none of them is repeated.) There are ways to arrange five distinct items (where the order of the arrangement matters.)

The reason is that there are five choices for the first item, four choices for the second item, three choices for the third item, etc. Hence, the numerator is , which is the same as . On the other hand, since there's only one way to choose five items out of five (i.e., to select them all,) the denominator would be .

Note that the is just one of that possible permutations. If the cards are arranged in random, all these permutations ought to have an equal probability. Therefore:

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it is probably the graph on the bottom right.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.