I need explination in details how did we calculate it

The Shannon Game intuition for perplexity - Josh Goodman: imagine a call-routing phone system gets 120K calls and has to recognize - "Operator" (let's say this occurs 1 in 4 calls) - "Sales" (1in 4) - "Technical Support" (1 in 4) - 30,000 different names (each name occurring 1 time in the 120K calls) We get the perplexity of this sequence of length 120Kby first multiplying 120K probabilities (90K of which are 1/4 and 30K of which are 1/120K ), nd then taking the inverse 120,000 th root: Perp=(1/41/41/41/41/4.1/120K1/120K.)(1/120K) But this can be arithmetically simplified to just N=4 : the operator (1/4), the sales (1/4), the tech support (1/4), and the 30,000 names (1/120,000) : Perplexity =((1/41/41/41/120K)(1/4)=52.6