Although factorial is an important tool in combinatorics and methods of counting, many of us are reluctant to use it beacuse of the odd-looking formula. (the sign itself asks you to exclaim ! 
) Using factorial and the formula is somewhat difficult to use in permutatons & combinations and hence, you can employ this method to calculate the value of nCr.
Here it goes ....
Suppose you have to find nCr ( or you have to SELECT r things out of n) :
for the numerator, write the product of r consecutive integers, beginning with n, each 1 less than the previous.
for the denominator, write the product of r consecutive integers beginning with 1, each 1 more than the previous.
For e.g calculate 6C3 :
step 1 : for the numerator, write the product of 3 consecutive integers, beginning with 6, each 1 less than the previous.
= 6 * 5 * 4 ( don't simplify. Let it be as the way it is).
step 2 : for the denominator, write the product of 3 consecutive integers beginning with 1, each 1 more than the previous.
= 1 * 2 * 3
therefore the value of 6C3 is numerator/denominator = (6 * 5 * 4) / (1 * 2 * 3) = 20
similarly, 4C2 = ( 4 * 3) / (1 * 2) = 6
Method to calculate nPr without factorials : (ARRANGEMENTS of n things taken r at a time)
Just write the product of r consecutive integers starting with n, each 1 less than the previous. That's it!
Suppose, you have to calculate the value of 5P3 :
Write the product of 3 consecutive integers starting with 5 each one less than the previous
= 5 * 4 * 3
P.S: In these methods, we've just jumped a step ahead in the calculation and avoided the factorial sign.
) Using factorial and the formula is somewhat difficult to use in permutatons & combinations and hence, you can employ this method to calculate the value of nCr.Here it goes ....
Suppose you have to find nCr ( or you have to SELECT r things out of n) :
for the numerator, write the product of r consecutive integers, beginning with n, each 1 less than the previous.
for the denominator, write the product of r consecutive integers beginning with 1, each 1 more than the previous.
For e.g calculate 6C3 :
step 1 : for the numerator, write the product of 3 consecutive integers, beginning with 6, each 1 less than the previous.
= 6 * 5 * 4 ( don't simplify. Let it be as the way it is).
step 2 : for the denominator, write the product of 3 consecutive integers beginning with 1, each 1 more than the previous.
= 1 * 2 * 3
therefore the value of 6C3 is numerator/denominator = (6 * 5 * 4) / (1 * 2 * 3) = 20
similarly, 4C2 = ( 4 * 3) / (1 * 2) = 6
Method to calculate nPr without factorials : (ARRANGEMENTS of n things taken r at a time)
Just write the product of r consecutive integers starting with n, each 1 less than the previous. That's it!
Suppose, you have to calculate the value of 5P3 :
Write the product of 3 consecutive integers starting with 5 each one less than the previous
= 5 * 4 * 3
P.S: In these methods, we've just jumped a step ahead in the calculation and avoided the factorial sign.
Regards,
Harsha
Harsha
