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rodikova [14]
3 years ago
7

Suppose that a teacher wishes to distribute 25 identical pencils to Ahmed, Barbara, Casper, and Dieter such that Ahmed and Diete

r receive at least one pencil each, Casper receives no more than five pencils, and Barbara receives at least four pencils. In how many ways can such a distribution be made?
Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
5 0

Answer:

we will change the problem in stages

pre-place 1 in x1 & x4, and 4 in x2, thus guaranteeing their minimum requirements.

now 19 pencils remain to be distributed

when there are no restrictions on distributing n identical objects to k distinct piles, the formula is (n+k-1)C(k-1) which here translates to 22C3

finally, we need to see that x3 = 5, so we place 6 in x3 (guaranteeing that it violates the condition), and subtract such violations, ie (22-6)C3 = 16C3

ans: 22C3 - 16C3 = 980

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At a shelter, 15% of the dogs are puppies. there are 60 dogs at the shelter. How many are puppies?
frutty [35]
So for this you need to find 15% of 60. There are a few ways to do this but I prefer to do it like this.

First, find 10% of 60. This can be found by dividing 60 by 10, because 100%/10% is 10.

This gives 10%=6

5% is half of 10%, so divide your answer for 10% (6), by 2.

This gives 5%=3

We needed 15%, so we add our 10% and 5% together, to get 9.

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Hope this helps!
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3 years ago
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It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly th
IRINA_888 [86]

Answer:0.0081  or 0.81%

Step-by-step explanation:

The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where

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p is the probability that one randomly selected calculator is defective= 10%=0.1

q is the probability that one randomly selected calculator is non-defective.

q=1-p=1-0.1=0.9

So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081

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Step-by-step explanation:

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3 years ago
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sveta [45]

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Step-by-step explanation:

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Ln e = 1, so:

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