1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider the following statements. I. Three letters can be posted in five letter boxes in 35 ways. II. In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is n - m P r - m × r P m Choose the correct option.

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Q. Consider the following statements.
I. Three letters can be posted in five letter boxes in $3^{5}$ ways.
II. In the permutations of $n$ things, $r$ taken together, the number of permutations in which m particular things occur together is ${ }^{ n - m } P _{ r - m } \times{ }^{ r } P _{ m }$
Choose the correct option.

Permutations and Combinations

Solution:

Both are false
I. Correct is $5^{3} (\because$ each one of the three letters can be posted in anyone of the five letter boxes.)
II. Statement will be true if $m$ particular things always occur.