Is this problem a combination or permutation? Suppose a group of 10 must pick an assistant, a representative, a treasurer, and a recorder. How many ways can this be done?

Permutation Problem

There are 5040 permutations possible

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Explanation:

Order matters because the positions are different.

(A,B,C,D) is different from (B,A,C,D) because the first means person A is the assistant while the second means person B is the assistant.

We have 10 choices for the first slot, 9 for the second, 8 for the third, and 7 for the fourth. We count down the values because a person cannot be reselected to serve multiple positions simultaneously.

Multiply out those values to get 10*9*8*7 = 5040

There are 5040 permutations possible.

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As an alternative, you can use the nPr permutation formula with n = 10 and r = 4 like so

We get the same answer as before.

Combination

Step-by-step explanation:

This is the answer because:

1) The difference between combinations and permutations is the ordering of each term.

Combinations - the order doesn't matter

Permutations - the order matters.

An example of this is, if you enter the number combination 5324 into your locker/cabinet, it won't open up because it is a different ordering and needs a specific combination which means it's permutation.  

2) In this situation, the order doesn't not matter since they just want different ways to select an assistant, a representative, a treasurer, and a recorder.

Hope this helps! :D

27/4x^6 y^8

step-by-step explanation:

4(3x^2y^4)^3 (2x^3y^5)^4

=

108x^6 y^12 /16x^12 y^20

=

108 /16x^6 y^8

=

27 /4x^6 y^8

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629