For the following exercises, compute the value of the expression. C(12, 4)

For the following exercises, compute the value of the expression.

C(12, 4)

Expert Solution

Consider the expression C(12, 4)

Use the general formula for combination,

C(n, r) = n!/r!(n – r)! ...... (1)

Substitute n = 12 and r = 4 in formula (1) C(n, r) = n!/r!(n – r)! and simplify,

C(12, 4) = 12!/4!(12 – 4)!

= 12!/4! × 8!

= (12 × 11 × 10 × 9 × 8!)/(4 × 3 × 2 × 1 × 8!)

= 495

Therefore, the value of the given expression is C(12, 4) = 495.

Junaid answered 2 years ago

For the following exercises, compute the value of the expression. C(8, 5)

For the following exercises, compute the value of the expression.C(8, 5)

For the following exercises, compute the value of the expression. C(26, 3)

For the following exercises, compute the value of the expression. P(11,5)

For the following exercises, compute the value of the expression.P(11,5)

Suppose N = 12 and r = 4. Compute the hypergeometric probabilities for the following values...

Suppose N = 12 and r = 4. Compute the hypergeometric probabilities for the following values of n and x. If the calculations are not possible, please select "not possible" from below drop-downs, and enter 0 in fields. a. n = 3, x = 2 (to 4 decimals). b. n = 2, x = 2 (to 4 decimals). c. n = 3, x = 0 (to 4 decimals). d. n = 6, x = 3 (to 4 decimals). e. n...

For the following exercises, write an explicit formula for each sequence. 4, 7, 12, 19, 28, …

C++ EXERCISES (a) Given int a = 5, b = 2, c = 4, and d...

C++ EXERCISES (a) Given int a = 5, b = 2, c = 4, and d = 5; determine the value of the expression: d % b * c > 5 || c % b * d < 7. (b) Which repetition statement is preferred for user data input and its validation? (c) Write a for statement to populate an array, double val[NUMCOUNT], for the following case: Use a counter named double count that has an initial value of 16.2,...

Problem 4-12 Future Value of an Annuity Find the future value of the following annuities. The...

Problem 4-12 Future Value of an Annuity Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by...

Javascript. Consider the following code fragment, that is supposed to compute the pixel value let c...

Javascript. Consider the following code fragment, that is supposed to compute the pixel value let c = image.getPixel(x, y); const m1 = (c[0] + c[1] + c[2]) / 3; c = image.getPixel(x + 1, y); const m2 = (c[0] + c[1] + c[2]) / 3; image.setPixel(x, y, [m1 - m2, m1 - m2, m1 - m2]); Give three pairs of pixel values (x, y) = [?, ?, ?] and (x+1, y) = [?, ?, ?] in the input image, for...

For the following exercises, graph the inequality. 1/4 x2 + y2 < 4

For the following exercises, graph the inequality.1/4 x2 + y2 < 4

In exercises 1–4, verify that the given formula is a solution to the initial value problem....

In exercises 1–4, verify that the given formula is a solution to the initial value problem. 2. Powers of t. b) y ′ = t^3 , y(0) = 5: y(t) = (1/5)t^(4) + 5 3. Sines and cosines. a) x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) = sint

Question