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noname [10]
3 years ago
14

A four-person committee is chosen from a group of eight boys and six girls.

Mathematics
2 answers:
Burka [1]3 years ago
7 0

The <em><u>correct answer</u></em> is:

C) 70/1001

Explanation:

Choosing 4 boys from a total of 8 boys is a combination of 8 taken 4 at a time:

_8C_4=\frac{8!}{4!4!}=70

Since they are all boys, we are choosing 0 girls from 6:

_6C_0=\frac{6!}{0!6!}=1

Choosing 4 students from 6+8=14 total students is a combination of 14 people taken 4 at a time:

_{14}C_4=\frac{14!}{4!10!}=1001

This gives us a probability of 70(1)/1001 = 70/1001.

QveST [7]3 years ago
4 0
70/1001 this is the answer because i just took the test so it is C.
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Take that formula and write in the numbers you know:

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Write the 5th term in the expansion of (5x-y/2)^7
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Answer:

65625/4(x^5)(y²)

Step-by-step explanation:

Using binomial expansion

Formula: (n k) (a^k)(b ^(n-k))

Where (n k) represents n combination of k (nCk)

From the question k = 5 (i.e. 5th term)

n = 7 (power of expression)

a = 5x

b = -y/2

....................

Solving nCk

n = 7

k = 5

nCk = 7C5

= 7!/(5!2!) ------ Expand Expression

=7 * 6 * 5! /(5! * 2*1)

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= 21 ------

.........................

Solving (a^k) (b^(n-k))

a = 5x

b = -y/2

k = 5

n = 7

Substituting these values in the expression

(5x)^5 * (-y/2)^(7-5)

= (3125x^5) * (-y/2)²

= 3125x^5 * y²/4

= (3125x^5)(y²)/4

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

Multiplying the two expression above

21 * (3125x^5)(y²)/4

= 65625/4(x^5)(y²)

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