1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ohaa [14]
3 years ago
8

In a shipment of 56 vials, only 13 do not have hairline cracks. If you randomly select 3 vials from the shipment, in how many wa

ys can at least one of the 3 selected vials have a hairline crack if the order of selection does not matter?
Mathematics
1 answer:
Elden [556K]3 years ago
5 0

Answer: 27434

Step-by-step explanation:

Given : Total number of vials = 56

Number of vials that do not have hairline cracks = 13

Then, Number of vials that have hairline cracks =56-13=43

Since , order of selection is not mattering here , so we combinations to find the number of ways.

The number of combinations of m thing r things at a time is given by :-

^nC_r=\dfrac{n!}{r!(n-r)!}

Now, the number of ways to select at least one out of 3 vials have a hairline crack will be :-

^{13}C_2\cdot ^{43}C_{1}+^{13}C_{1}\cdot ^{43}C_{2}+^{13}C_0\cdot ^{43}C_{3}\\\\=\dfrac{13!}{2!(13-2)!}\cdot\dfrac{43!}{1!(42)!}+\dfrac{13!}{1!(12)!}\cdot\dfrac{43!}{2!(41)!}+\dfrac{13!}{0!(13)!}\cdot\dfrac{43!}{3!(40)!}\\\\=\dfrac{13\times12\times11!}{2\times11!}\cdot (43)+(13)\cdot\dfrac{43\times42\times41!}{2\times41!}+(1)\dfrac{43\times42\times41\times40!}{6\times40!}\\\\=3354+11739+12341=27434

Hence, the required number of ways =27434

You might be interested in
A small child is at a candy store, eager to spend his $1 allowance on candy. His two favorite candies are priced at $0.05 and $0
kumpel [21]
A would probably be the answer
4 0
3 years ago
What factors of 48 are multiples of 4
lorasvet [3.4K]
<span>4, 8, 12, 16, 24, 48</span>
8 0
3 years ago
Read 2 more answers
A group of scientists have been sent on an expedition to test the soil in the Allegheny Mountains. They need to collect samples
3241004551 [841]
It’s B. 52 units ...
9 0
2 years ago
Read 2 more answers
(Will Mark Brainliest!!!)Choose the point-slope form of the equation below that represents the line that passes through the poin
krek1111 [17]

Answer:

b

Step-by-step explanation:

the point-slope form of the equation is equal to

6 0
3 years ago
Can u please answer all three and in 20-30 minutes please or quicker if u can please I just not understanding the math they are
Jlenok [28]

18).  16:80 is the ratio but in simplest form is; 5:0

19).   36:54 is the ratio but in simplest form is; 2:3

20).   12:24 is the ratio but in simplest form is; 1:2

hope that helps:D

5 0
3 years ago
Other questions:
  • How do you use a number line to solve 58+19
    10·1 answer
  • Please help (look @ pic)
    15·1 answer
  • Help help quickly!!!!!
    7·2 answers
  • Miguel opened a savings account with S200 and was paid simple interest at an annual rate of 6%. When Miguel closed the account,
    13·1 answer
  • If your Disney vacation cost $5,026 and you normally make $20 per hour, how many total DAYS of overtime will you need to work to
    5·1 answer
  • Find the solution set:
    6·2 answers
  • Rafael spins the pointers of the two spinners shown at the right. Find the probability of each possible sum.
    10·1 answer
  • Calculate the average rate of change of
    5·1 answer
  • Need quick help with this math
    7·2 answers
  • Simplify the expression:<br> 2f + 10 + 7 + 3
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!