Q.In a market survey of 200 shoppers in Bhubaneswar, 90 use UPI, 70 use debit cards, and 60 use cash. Of these, 30 use both UPI and debit card, 25 use both debit card and cash, 20 use both UPI and cash, and 10 use all three payment methods. Find

Add all three individual counts, subtract each pairwise overlap once, then add back the triple overlap that was subtracted too many times.

Step 1 — Identify the sets. $A$=UPI users, $n(A)=90$; $B$=debit-card users, $n(B)=70$; $C$=cash users, $n(C)=60$. Pairwise: $n(A\cap B)=30$, $n(B\cap C)=25$, $n(A\cap C)=20$. Triple: $n(A\cap B\cap C)=10$. Total surveyed $=200$.

Step 2 — Apply the three-set inclusion-exclusion formula.

Step 3 — Find the "none" group. Shoppers using none of the three methods: $200-155=45$. …

Building the full seven-region Venn breakdown (three "only" regions, three "exactly two" regions, one "all three" region) and summing them …

Forgetting to add back $n(A\cap B\cap C)$ at the end — shoppers using all three get subtracted once within each of the three pairwise terms (three times total), so the …