Can someone please tell me the logic behind the square of p_i in the power of the exponent of the answer

4.62. Consider n independent trials, each of which results in one of the outcomes 1,.. ,k with respective probabil- ities p1. .Pk 2Pi = 1. Show that if all the p; are small, then the probability that no trial outcome occurs more than once is approximately equal to exp(-n(n - 1) LiP/2).