Determine the amount of combinations of:

Question

i) 7 things taken 4 at a time.

ii) 9 things take 6 at a time.

iii) 5 things taken 5 at a time.

Answer 1

i) Choice of 1st selection is 7, leaving 6; 2nd selection 6, leaving 5; 3rd selection 5, leaving 4; 4th selection 4. Combine these: 7×6×5×4=840 permutations. But these permutations include all possible arrangements of 4 different objects, so since there are 4×3×2×1=24 ways of arranging the same combination of objects we need to divide 840 by 24=35 to find out how many unique combinations there are. Another way of writing this is ⁷C₄=35.

ii) ⁹C₆=84.

iii) There is only one way of combining all 5 objects.