could you check is that right? Instructions: Print your name nd ID above. You mu

Question

could you check is that right?

Instructions: Print your name nd ID above. You must work alone and you can use a basic calculator. The point-value of each question is indicated in brackets at the beginning of the question. There are a marimum o 57 points possible (7 bonus points). Show your work in the space provrded. If you questions that clearly require it, then you may not receive full credit. do not show al your work on 10 In each part of this question, you are counting the number of four-letter arrangements using the letters of BANGOLDRIC subject to the various stated restrictions. Remember, the only restrictions are the stated ones. In each part below, you need to first decide how many cases you havwe. 1. a) How many such arrangements have one vowel and three different consonants [Hint: Four cases depending on where the vowel is] Vowe l A01 1-840 25 2 0 b) How many contain one vowel and three different consonants, and begin with the letter G and end with the letter D -7 30 c) How many begin with two consonants frors BRAND, and end with two vowels from LOGIC. BRND PROI NDOT RNOI BD As stated in the course syllabus, in 2013 the dean of the Eberly College of Sciences at Penn State University announced a commitment to implement ethics into the undergraduate science curriculum Although we have not discussed this in lecture, to contribute to their initiative, a few of the questions on this test (like exercises in your text) have a context with ethical considerations.

Explanation / Answer

There are 3 vowels and 7 consonants

I do it by the box method. Its easier but in this case we need to check your answers.

(a)

Therefore 3 x 7 x 6 x 5 = 630 and I can position the vowels and consonants in 4 ways in 4 ways VCCC, CVCC, CCVC, CCCV.

Therefore total number of ways = 630 * 4 = 2520. Your answer is correct.

(b) Starts and ends with G and D repectively. So 5 consonants remain.

So

= 5 x3 = 15 ways. But I can also have

= 5 x 3 = 15 ways

Therefore total ways is 30. Your answer is correct.

(c) First 2 letters should be 2 consonants from BRAND. Brand has 4 consonants. The last 2 letters should be vowels from LOGIC. LOGIC has 2 vowels.

Therefore 4 x 3 x 2 x 1 = 24 ways. Your answer is correct.

Your explanations are also correct.

Any 3 vowels any 7 consonants Any 6 remaining consonants Any 5 remaining consonants

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