I do not have an nCr or nPr button on my calculator. How can I do the calulations 'by hand'? |
Use the formula .
For example,
Note how you can "cancel in chunks" top and bottom to simplify the fraction.
Use the formula .
For example,
There is an even quicker way if can remember it . . .
^{n}C_{r} is a fraction with r! on the bottom and the same number of whole numbers starting from n multiplied down in steps on 1 on the top.
For example,
Remember to use symmetry to keep the numbers small:
^{10}C_{6} is the same as ^{10}C_{4}
^{12}C_{9} is the same as ^{12}C_{3}
^{15}C_{13} is the same as ^{15}C_{2} , etc
^{n}P_{r} is found by ^{n}C_{r} multiplied by r!