Solve the problem.
-List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2)?
A)ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef C(6, 2)= 15
B)ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe C(6, 2)= 30
C)aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fb, fc, fd, fe, ff
C(6, 2)= 36
D)ab, ac, ad, ae, bc, bd, be, cd, ce, cf, de, df C(6, 2)= 12

Question

Quizplus · Accepted Answer

The problem asks for combinations taken 2 at a time, which means we don't count combinations like "aa" or "ba" where the objects are repeated or the order is different. We use the formula for combinations, C(n, r) = n!/(r!(n-r)!) where n is the total number of objects and r is the number of objects we are choosing. So in this case, C(6,2) = 6!/[(2!)(6-2)!] = 15. Looking at the choices, only option A has 15 combinations listed. C(6, 2) represents the number of ways of choosing 2 objects from a set of 6 objects without repetition and order. The formula for C(n, r) is n! / (r!*(n-r)!), where n is the total number of objects and r is the number of objects to choose. From the given options, choice A is the one that lists all possible combinations of 2 objects taken from a set of 6 objects. This list contains 15 items, which matches the value of C(6, 2), so the answer is A.

Solve the Problem. -List All the Combinations of 6 Objects A, B, C