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oksian1 [2.3K]
3 years ago
11

So I have to compute the following but i don't know what they mean any help?

Mathematics
2 answers:
Gelneren [198K]3 years ago
7 0

Answer:

Step-by-step explanation:

This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr

i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.

I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.

Recall that

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

Consider question a) we are given (5 1) or ₅C₁

we can see that n = 5 and r = 1

If we substitute this into the formula:

₅C₁ = (5!) / [ (1!)(5- 1)!]

= (5!) / [ (5- 1)!]

= (5!) / (4!)

= (5·4·3·2·1) / (4·3·2·1)

= 5

hence ₅C₁ = 5

timama [110]3 years ago
4 0

Answer:

(a) 5

(b) 10

(c) 35

(d) 28

(e) 9

(f) 21

Step-by-step explanation:

(\frac{n}{k} )=\frac{n!}{k!(n-k)!}

(a)

(\frac{5}{1} )=\frac{5!}{1!(5-1)!} \\\\(\frac{5}{1} )=\frac{5*4*3*2*1}{1*4!} \\\\(\frac{5}{1} )=\frac{120}{1*4*3*2*1} \\\\(\frac{5}{1} )=\frac{120}{24} \\\\(\frac{5}{1} )=5

(b)

(\frac{5}{3} )=\frac{5!}{3!(5-3)!} \\\\(\frac{5}{3} )=\frac{5*4*3*2*1}{3*2*1*2!} \\\\(\frac{5}{3} )=\frac{120}{3*2*1*2*1}\\\\(\frac{5}{3} )=\frac{120}{12} \\\\(\frac{5}{3} )=10

(c)

(\frac{7}{4} )=\frac{7!}{4!(7-4)!} \\\\(\frac{7}{4} )=\frac{7*6*5*4*3*2*1}{4*3*2*1*3!} \\\\(\frac{7}{4} )=\frac{5040}{4*3*2*1*3*2*1} \\\\(\frac{7}{4} )=\frac{5040}{144} \\\\(\frac{7}{4} )=35

(d)

(\frac{8}{2}) =\frac{8!}{2!(8-2)!} \\\\(\frac{8}{2}) =\frac{8*7*6*5*4*3*2*1}{2*1*6!} \\\\(\frac{8}{2}) =\frac{40320}{2*1*6*5*4*3*2*1}\\\\(\frac{8}{2}) =\frac{40320}{1440} \\\\(\frac{8}{2}) =28

(e)

(\frac{9}{8} )=\frac{9!}{8!(9-8)!} \\\\(\frac{9}{8} )=\frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1} \\\\(\frac{9}{8} )=\frac{362880}{40320} \\\\(\frac{9}{8} )=9

(f)

(\frac{10}{4} )=\frac{10!}{4!(10-4)!} \\\\(\frac{10}{4} )=\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6!} \\\\(\frac{10}{4} )=\frac{3628800}{24*6*5*4*3*2*1} \\\\(\frac{10}{4} )=\frac{362880}{17280} \\\\(\frac{10}{4} )=21

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8 0
3 years ago
please help me and before you try to answer the height is not 8 in but the volume is 25.12 in if that helps thank you <3
DochEvi [55]

Answer:

25.12 in^3.

Step-by-step explanation:

Volume of the cylinder = 3.14 * r^2 * h

= 3.14 * 2^2 * 8

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= 1/4 * 3.14 * 4 * 8

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3 0
3 years ago
Read 2 more answers
FAST PLEASE VERY INPORTANT
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-24°F

Step-by-step explanation:

-18°F + 13°F - 19°F

= -5°F - 19°F

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5 0
2 years ago
Read 2 more answers
If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to support your an
katen-ka-za [31]
Pam and her brother both open savings accounts. each begin with a balance of $0. For every $2 is that Pam saves in her account her brother saves $5 in his account

P:bro=2:5
when P=40 what is bro?

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8 0
3 years ago
There are visitors at home. Michelle made 10 and 3/5 cups of tea while Leslie made 9 and 2/5 cups of tea. How many cups of tea d
Rufina [12.5K]

Answer:

20 cups

Step-by-step explanation:

Michelle: 10 3/5 cups made

Leslie: 9 2/5 cups made

<u>Steps:</u>

<em>First, let's turn each number into decimal form.</em>

10 3/5 = 10.6

9 2/5 = 9.4

<em>Then, add</em>

9.4 + 10.6 = 20

<em>Conclusion</em>

They made 20 cups in all

Note:

Hope this helped :)

Have a nice day

Reply with any questions or concerns please :D

6 0
2 years ago
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