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klemol
3 days ago
11

In regional spelling bee, the 8 finalists consist of 3 boys and 5 girls. Find the number of sample point the sample space S for

the number of possible orders at the conclusion of the contest for:
- All 8 finalist
- The fist 3 positions
Mathematics
1 answer:
PIT_PIT [9.1K]3 days ago
3 0

Answer:

i) A total of 40320 different arrangements

ii) For the initial 3 spots, there are 336 different combinations.

Step-by-step explanation:

Given: The total finalists = 8

The count of boys = 3

The count of girls = 5

To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!

The number of possible arrangements equals 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.

nPr =\frac{n!}{(n - r)!}

Here n = 8 and r = 3

Substituting n = 8 and r = 3 into the formula, we arrive at

8P3 = \frac{8!}{(8 - 3)!}

= \frac{8!}{5!} \\= \frac{1.2.3.4.5.6.7.8}{1.2.3.4.5}

= 6.7.8

= 336

Thus, there are 336 different arrangements for the first 3 spots.

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Answer:

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Step-by-step explanation:

The initial scenario is a specific case of the subsequent one, so we will address the second case first.

Consider y = A\sin(kt) + B\cos(kt). Through the utilization of derivatives and trigonometric function properties, it is determined that

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The equation is represented as 81y''=-4y. It's important to note that since y'' = -k^2y it leads to the equation

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It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.

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The question is not properly framed

Complete Question

Identify all decimals equivalent to ( 9 × 100 ) + ( 2 × 10 ) + ( 3 × 1/10 ) + ( 5 × 1/100 ). A. 92.35 B. 920.350 C. 902.35 D. 92.350 E. 920.35 F. 920.035

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E. 920.35

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Step 2

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