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Elanso [62]
3 years ago
14

How many different committees can be formed from 12 teachers Abs 43 students of the committee consists of 4 teachers and 3 stude

nts ? In how many ways can the committee of 7 members be selected ?
Mathematics
1 answer:
Marina86 [1]3 years ago
3 0

Answer:

6108795

Step-by-step explanation:

To obtain the number of ways the committee can be selected :

4 teachers from the 12 teachers available and 3 students from the 43 students available

Using combinatorics :

12C4 * 43C3

recall :

nCr = n! ÷ (n - r)!r!

Using calculator :

12C4 = 495

43C3 = 12341

12C4 * 43C3

495 * 12341

= 6108795

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Step-by-step explanation:

See the diagram attached below which describes and represents the information given to us.

The tangents are PA and PB.

Tangents form right angle with the radius of a circle, therefore:

<OBP = <OAP = 90°

Therefore ∆OBP is a right triangle.

m<APO = m<BPO = ½(60) = 30°

Thus, in ∆OBP,

Reference angle = 30°

Side length opposite to reference angle = 12 ft

Adjacent length = length of tangent PB

Apply trigonometric function TOA, to find PB:

Tan 30 = Opp/Adj

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PB × Tan 30 = 12

PB = 12/Tan 30

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Length of each segment = 20.7 ft

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