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.

Question

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. (A) Only I is false. (B) Only II is false. (C) Both are false. (D) Both are true.

Tardigrade Admin · Accepted Answer

Both are false I. Correct is 53 (∵ 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.

Q. 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−mPr−m​×rPm​ Choose the correct option.

Only I is false.

Only II is false.

Both are false.

Both are true.

Both are false I. Correct is 53(∵ 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.

Both are false
I. Correct is $5^{3} (∵$ 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.