The no.of ways in which 4 letters can be posted in 5 letter boxes is45ways II. If words are formed by taking only 4 at a time out of the letters of the word PHYSICS, then the number of words in which Y occur is 288 . Which of the above statements is correct?Only IOnly IIBoth I and IINeither I nor II

To determine which statement is correct, let's analyze each statement separately:

Statement I: "The number of ways in which 4 letters can be posted in 5 letter boxes is 45 ways."

To solve this problem, we can use the concept of combinations. The number of ways to choose 4 letters out of 5 letter boxes can be calculated using the formula for combinations, which is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.

In this case, we have 5 letter boxes and we want to choose 4 letters. So, the number of ways is 5C4 = 5! / (4!(5-4)!) = 5.

Therefore, statement I is incorrect. The correct number of ways in which 4 letters can be posted in 5 letter boxes is 5 ways, not 45.

Statement II: "If words are formed by taking only 4 at a time out of the letters of the word PHYSICS, then the number of words in which Y occurs is 288."

To solve this problem, we need to consider the word "PHYSICS" and find the number of words that can be formed by taking only 4 letters at a time.

The word "PHYSICS" has a total of 7 letters. To find the number of words that can be formed by taking 4 letters at a time, we can use the concept of combinations again. The number of ways to choose 4 letters out of 7 letters can be calculated as 7C4 = 7! / (4!(7-4)!) = 7! / (4!3!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

However, statement II states that the number of words in which the letter "Y" occurs is 288. Since 288 is not equal to 35, statement II is also incorrect.

Therefore, the correct answer is "Neither I nor II" as both statements are incorrect.