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True [87]
2 years ago
8

Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people c

an be made if:
a) there must be exactly 3 students on the committee

b) there must be at least one teacher and at least one student on the committee
Mathematics
1 answer:
mariarad [96]2 years ago
4 0

Answer:

a) 11,880

b) 7,770

Step-by-step explanation:

The number of teachers that volunteer = 6 teachers

The number of students that volunteer = 12 students

The number of people in the committee = 5 people

a) The exact number of student on the committee = 3 student

Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2

The number of teachers in the committee = 2 teachers

We get;

The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880

b) When there is at least one teacher and at least one student on the committee, we have;

₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770

The number of committees having at least one teacher and at least one student = 7,770

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Answer:

Owl= 67.14ft

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

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Considering Jason's position:

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Where x = distance between the tree and Alison

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Considering Alison's position

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H = H

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Open bracket

x *0.4068 + 48 *0.4068 = 0.5932x

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Collect Like Terms

-0.5932x+0.4068x = -19.5264

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0.1864x = 19.5264

Make x the subject

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Substitute 104.76 for x in H = xtan(30.675^{\circ})

H = 104.76 * tan(30.675^{\circ})

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