Question

The maximum number of persons in a country in which no two persons have an identical set of teeth assuming that there is no person without a tooth is

• A. $2{}^3{}^2$
• B. $2{}^3{}^2$ $-1$
• C. $32!$
• D. $32!-1$

Answer 1

The correct option is B $2{}^3{}^2$ $-1$

Total no. of teeth a person has = 32

No. of persons having 1 tooth is =$32C_1$

No. of persons having 2 tooth is = ${{}^{32}C}_2$

No. of persons having 3 tooth is = ${{}^{32}C}_3$

...... and so on ..... 32 tooth = ${{}^{32}C}_{32}$

Total persons = ${}^{32}{C}_1+{{}^{32}C}_2+{{}^{32}C}_3........+{{}^{32}C}_{32}=2^{32}-1$