Question

I need to pick 4 apples out of 10 . Why is the answer 10C4 and not 10C1.9C1.8C1.7C1 ? Why is it wrong ?

Answer 1

u need to pick four....... but not mentioned one by one

Answer 2

Say , I pick one by one , at the end I have 4 only . What is the difference in these two situations ?

Answer 3

On calculating , I am getting more possibilites for the 10C1.9C1.8C1.7C1 situation . What extra am I counting ?

Answer 4

You're looking at the group of apples you have at the end... after you've selected four of them, and what the question is asking is how many distinct groups of 4 apples do you have?

Answer 5

because the group {2,3,5,7} is the same as the group {3,2,7,5} we have to use combinations.

permutations take into account the order, combinations do not.

Answer 6

you method is getting a particular sequence... a permutation. however, as previously stated, the order in which the items in the group are selected is not important, merely which items are in the group.

Answer 7

Ahaaa ! I see !

Answer 8

\[_{10}C_{4} = \frac{ _{10}P_4 }{ 4! }\]

we divided the number of distinct arrangements by the number of ways we can arrange the selected items (the 4 apples). this is because we count
{2,3,5,7} the same as all other arrangements of these 4 elements.

so {2,3,5,7} is the same as:
{2,5,3,7}, {2,5,7,3}, {2,7,3,5}, {2,7,3,5}, etc.

Answer 9

Right on!!!

Answer 10

Got it !
Thanks a ton :) :)

Answer 11

remember to ask yourself these 2 questions when considering permutations vs. combinations:

1st. Are you sampling (selecting items) with or without replacement. That is, are the same items available for selection after you have selected 1 or more.

2nd. Does the order in which you select items matter? That is, if you select 2 (or more) items, would ({a,b} be the same as {b,a}? If so, it's combinations; if not, permutations (providing you are sampling without replacement).

Answer 12

you're welcome!

Answer 13

Will surely keep the two points in my mind in the future :)