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
tekilochka [14]
1 year ago
9

How many different ways are there to choose a subset of the set {1,2,3,4,5,6} so that the product of the members of the subset i

s even
Mathematics
1 answer:
zvonat [6]1 year ago
3 0

You have to pick at least one even factor from the set to make an even product.

There are 3 even numbers to choose from, and we can pick up to 3 additional odd numbers.

For example, if we pick out 1 even number and 2 odd numbers, this can be done in

\dbinom 31 \dbinom 32 = 3\cdot3 = 9

ways. If we pick out 3 even numbers and 0 odd numbers, this can be done in

\dbinom 33 \dbinom 30 = 1\cdot1 = 1

way.

The total count is then the sum of all possible selections with at least 1 even number and between 0 and 3 odd numbers.

\displaystyle \sum_{e=1}^3 \binom 3e \sum_{o=0}^3 \binom 3o = 2^3 \sum_{e=1}^3 \binom3e = 8 \left(\sum_{e=0}^3 \binom3e - \binom30\right) = 8(2^3 - 1) = \boxed{56}

where we use the binomial identity

\displaystyle \sum_{k=0}^n \binom nk = \sum_{k=0}^n \binom nk 1^{n-k} 1^k = (1+1)^n = 2^n

You might be interested in
Write the equation of a line with a slope of 3 and a y-intercept of 1.
posledela
Y = mx + b is the equation

m = slope, or 3
b = y-intercept, or 1

y = 3x + 1
is your equation
6 0
3 years ago
A) Rate (R)<br>24/5<br>Time = 1 month<br>Interest = Rs. 39.96​
yKpoI14uk [10]

Answer:  P = $ 1,998.01

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 24%/100 = 0.24 per year,

putting time into years for simplicity,

1 months ÷ 12 months/year = 0.083333 years,

then, solving our equation

P = 39.96 / ( 0.24 × 0.083333 ) = 1998.007992032

P = $ 1,998.01

The principal required to

accumulate interest of $ 39.96

on a rate of 24% per year for 0.083333 years (1 months) is $ 1,998.01.

5 0
3 years ago
Help me on this quiz
kolezko [41]

The Answer For Number Two Is Negative 14

7 0
2 years ago
Apply the distributive property to create an equivalent expression.<br> −9⋅(5j+k)
disa [49]

Step-by-step explanation:

step one: *multiply the negative 9 with the 5j.

which which will come out to be -45j

step 2: now now multiply the -9 with the k. which it comes out to be negative 9k.

step 3: -45j + -9k

4 0
3 years ago
Read 2 more answers
???????????????????????????
FinnZ [79.3K]

Answer:

y-(-20)=1(x-(-10))

Step-by-step explanation:

If you're really in college you should know this, but here's the explanation:

m= <u>-9-(-20)</u>

      1-(-10)

  = <u>11</u>

     11

m = 1

The equation is y-y^1=m(x-x^1)

Replace the y^1, m, and x^1 from the first point

You get y-(-20)=1(x-(-10))

Or simplify that into y+20=x+10

You can also simplify it more but I don't think you need that for that question

7 0
2 years ago
Other questions:
  • HELP PLEASE‼️‼️ the questions are on the photo
    9·1 answer
  • Please help asap 25 pts
    9·2 answers
  • What is the value of x in this simplified expression? (-j)^-7=1/(-j)^x
    8·1 answer
  • How many obtuse angel does the triangle have
    14·1 answer
  • What is the image of the point (0,9) after a rotation of 90° counterclockwise about<br> the origin?
    7·1 answer
  • 19 = 15 w- 4(3 w-1) solve for w
    15·1 answer
  • 2+9n=72<br> how do you find what n equals?
    6·1 answer
  • Complete the function table.
    11·1 answer
  • Expand the following :<br><br>A) 2(x+3)<br><br>B) 5(2x-4)<br><br>C) 4(2x+1)<br><br>D) 6(x-4y)​
    8·1 answer
  • M
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!