Question

Thirty-six people in student council are running for the offices of president and vice-president. In how many different ways can those offices be assigned?



1,260

578

71

Answer 1

36 P 2

Answer 2

\[\large{^{36}C_{2} \times 2!}\]

Answer 3

C - combination
P - permutation

Answer 4

ok so how do i do a combo

Answer 5

\[\large{^n C_{r} = \cfrac{n!}{r!(n-r)!}}\]

Answer 6

\[\large{^n P_r = \cfrac{n!}{(n-r)!}}\]

Answer 7

Actually:

\[\large{^{36} P_{2} = ^{36}C_{2} \times 2!}\]

Answer 8

ok thank you

Answer 9

:) Your welcome

Answer 10

hmm

Answer 11

C - choosing

P - arranging

(another way of understanding)

You can either directly arrange 2 people out of 36 - 36P2

OR

Choose 2 out of 36 and then arrange them - 36C2 * 2!

Answer 12

so would it be 578?

Answer 13

36 choices for president
one that is chosen 35 for veep
by the counting principle the number of ways to do this is \(36\times 35\)
do not get married to any formulas

Answer 14

1260

Answer 15

Both are same @satellite73

Answer 16

all these formulas are based on formalizing the counting principle for different scenarios
think
don't be a slave to the formulas

Answer 17

Ok, that makes a bit more scense

Answer 18

\[\large{^{36} C_{2} \times 2! = \cfrac{36!}{34!} = 36*35 = 1260}\]

Answer 19

I agree with @satellite73 . Don't use formulas unless necessary. When you can solve the problems without them then go for it

Answer 20

yes, i know both are the same
but it is clear that 36 choices followed by 36 choices gives \(36\times 35\) choices based on nothing more than common sense and the counting principle
no formulas needed
no factorials
nothing of the kind

Answer 21

typo there but you get the idea

Answer 22

Correct ^^^

Special cases/formulas are useless if you have the basic concepts correct

Answer 23

Though remember this:

@satellite73 used `36 * 35` because it is an AND operation. You have to choose president AND vice- president

Answer 24

vishweshshrimali5 , why do write \(\normalsize\color{blue}{ ~^{\LARGE36}P_{\LARGE2} }\) instead of \(\normalsize\color{blue}{ ~_{\LARGE36}P_{\LARGE2} }\) ?

Answer 25

Similarly, I too used `36C2 * 2!` because I have to choose 2 people out of 36 AND then I have to arrange them

Answer 26

That is notation I have always read and studied :)

Answer 27

further, even \(\binom{n}{k}\) should not be formula driven
imagine computing
\[\binom{100}{2}\] when all that is required is \[\frac{100\times 99}{2}\]

Answer 28

Yep :)

Answer 29

thanks you guys, you both have been a great help

Answer 30

Things are easier to understand and solve when you know the "WHY"

Answer 31

Your welcome @CLoudrunner :)

Answer 32

@SolomonZelman i have never seen \(_nC_k\) or \(^nC_k\) in a text
only \(\binom{n}{k}\)

Answer 33

I have seen both \(\large{^nC_k}\) and \(\large{\binom{n}{k}}\) - this one in foreign writers' books