In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than $32$ teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city is
In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than $32$ teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, then the maximum population of the city is
- A
${2^{32}}$
- B
${(32)^2} - 1$
- C
${2^{32}} - 1$
- D
${2^{32 - 1}}$
Similar Questions
The number of four letter words that can be formed using the letters of the word $BARRACK$ is
- [JEE MAIN 2018]
If for some $\mathrm{m}, \mathrm{n} ;{ }^6 \mathrm{C}_{\mathrm{m}}+2\left({ }^6 \mathrm{C}_{\mathrm{m}+1}\right)+{ }^6 \mathrm{C}_{\mathrm{m}+2}>{ }^8 \mathrm{C}_3$ and ${ }^{n-1} P_3:{ }^n P_4=1: 8$, then ${ }^n P_{m+1}+{ }^{n+1} C_m$ is equal to
If for some $\mathrm{m}, \mathrm{n} ;{ }^6 \mathrm{C}_{\mathrm{m}}+2\left({ }^6 \mathrm{C}_{\mathrm{m}+1}\right)+{ }^6 \mathrm{C}_{\mathrm{m}+2}>{ }^8 \mathrm{C}_3$ and ${ }^{n-1} P_3:{ }^n P_4=1: 8$, then ${ }^n P_{m+1}+{ }^{n+1} C_m$ is equal to
- [JEE MAIN 2024]
The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is
The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is
- [KVPY 2019]
$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $
$^n{C_r}\,{ \div ^n}{C_{r - 1}} = $
$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated is
$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$, then the number of ways in which they can be seated is
- [IIT 1983]