A train consists of n carriages and there are P passengers. Each one of the P passengers randomly selects the carriage in which he will ride. On the basis of above information, answer

$^{n} C_{1} 1^{p} -^{n} C_{2} 2^{p} +^{n} C_{3} 3^{p} . . . . + (- 1)^{n - 1 n} C_{n} n^{p}$ is equal to,

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If "n" number of H3PO4 molecules are polymerized to produce chain molecule and ring molecule separately, then the number of P−O−P linkages formed is, respectively :

The correct option is C (n−1) and nIn case of a ring, the number of linkages will be one less than the number of P atoms because of the fact that each P atom is shared by 2 rings.However, in case of a chain no sharing takes place and the number of linkages is equal to n.

If " $n$ " number of $H_{3} P O_{4}$ molecules are polymerized to produce chain molecule and ring molecule separately, then the number of $P - O - P$ linkages formed is, respectively :

The correct option is C $(n - 1)$ and $n$
In case of a ring, the number of linkages will be one less than the number of $P$ atoms because of the fact that each $P$ atom is shared by $2$ rings.
However, in case of a chain no sharing takes place and the number of linkages is equal to $n$ .