Combinations

[Cook10]

Lindsey is shopping for clothes and finds that there are nine different items in her size at the store. In how many ways can Lindsay make a purchase?

 

[pka]

Lindsey is shopping for clothes and finds that there are nine different items in her size at the store. In how many ways can Lindsay make a purchase?

If \(n\) is a positive integer then \(\mathcal{C}_1^n=n\)

 

[Deleted member 4993]

Lindsey is shopping for clothes and finds that there are nine different items in her size at the store. In how many ways can Lindsay make a purchase?

Lindsey can purchase 1 dress in \(\displaystyle C^9_1 \)(=9) ways

Lindsey can purchase 2 dresses in \(\displaystyle C^9_2 \) (=36) ways

and continue......

 

[Steven G]

Is it making a purchase if you buy nothing?

Note that 2^n = _nC₀ + _nC₁ + _nC₂ + ... + _nC_n

 

[pka]

Linguist may differ with me on this but making a purchase from nine items means buying one.
If on the other hand like my daughter, faced with nine dresses then buying anywhere from one to all nine is likely.
There are \(2^9-1=511\) different possible purchases possible. In a set of \(9\) members there are \(2^9=512\) possible subsets.
However that includes the null set which evolves no purchase. Thus there can be only \(511\) different purchases.
But I am absolutely sure that this question meant the buying of one dress. Otherwise, it was not written by a professional in the area.