6 is the total number of all possible combinations for choosing 1 elements at a time from 6 distinct elements without considering the order of elements in statistics & probability surveys or experiments. The number of combinations for sample space 6 CHOOSE 1 can also be written as 6C1 in the format of nCr or nCk.

The number of 5-digit combinations is 10 5=100,000. So, one more than 99,999. You can generalize that: the number of N-digit combinations is 10 N. Now, this assumes that you count 00000 or 00534 as “5-digit numbers”.

The difference between combinations and permutations is ordering. With permutations we care about the order of the elements, whereas with combinations we don’t. For example, say your locker “combo” is 5432. If you enter 4325 into your locker it won’t open because it is a different ordering (aka permutation).

26⋅26⋅26=263=17576. If you want the letters to be unique, the calculation changes slightly.

6C3 = the number of combinations of three one can choose from a pool of six unique items. So, it turns out, there are twenty ways to pick a set of three items from a pool of six unique items. That’s one way to calculate nCr, but it’s not the only way.

where n is the number of items and r is the unique arrangements.

1. Plugging in our numbers of n = 6 and r = 3, we get:
2. Calculate the numerator n!:
3. Calculate the first denominator (n – r)!:
4. Calculate the second denominator r!:
5. Calculate our combination value nCr for n = 6 and r = 3:

In short, it is the number of ways to choose two elements out of n elements. For example, ‘4 choose 2’ is 6. If I have four elements – A, B, C and D – I can select two elements in the following ways – {A, B}, {A, C}, {A, D}, {B, C}, {B, D} and {C, D}.

1. 6P3 means the number of permutations of six objects taken three at a time.

Answer Expert Verified A permutation is a type of combination where order is important. The only one of these choices where some ranking is involved is C, the positions of president, vice president and treasurer.

(n – r)! nCr =n! / r! (n – r)! = 6! / 3!…Thank you.

step 3 Find the factorial for 11!, 7! & 4!, substitute the corresponding values in the below expression and simplify. 11C7 = 11!