A Combination is an arrangement of items in which order does not matter. To find the number of Combinations of n items chosen r at a time, you can use the formula

n^{C}r = n!/r!(n-r)! where 0 ≤ r ≤ n

A class consists of 14 boys and 17 girls. Four students from the class are to be selected to go on a trip.

(a) How many different possibilities are there for the 4 students selected to make the trip?

(b) If it has been decided that 2 boys and 2 girls will make the trip, then in how many different ways could the 4 students be selected?

**Solution**

(a) C(31,4) = = 31,465

(b) C(14,2) ! C(17,2) = 91 ! 136 = 12,376

Number of combinations: The number of all combination of n things, taken r at a time is:

nCr=n!/R!(n-1)! = (n(n-1)(n-2)….to r factors)/r!

An Important Result:

nCr=1 and nCr = nC(n-r)

Example:

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