Consider the following statements:

a. The number of ways to arrange the letters of the word "PEPPER" is 60

b. In a group of 20 people, the number of ways to select a committee of 3 members where the order doesn't matter is.

c. The expansion of (2+x)³ using binomial theorem is 8+6x+12x²+x³.

d. The number of ways 3 boys and 3 girls are sit in a row is 360.

Which of the following statement is correct?

Statement a (Correct):

The word PEPPER consists of six letters in total, where the letter P appears three times and the letter E appears two times. To find the total number of unique arrangements, you take the factorial of the total number of letters (six factorial, which equals seven hundred twenty) and divide it by the factorials of the repeated letters (three factorial times two factorial, which equals twelve). Dividing seven hundred twenty by twelve gives exactly sixty. Therefore, this statement is completely accurate.

Statement b (Incorrect):

This statement is cut off and incomplete at the end. For reference, the actual number of ways to select a committee of three members from a group of twenty people where order does not matter is one thousand one hundred forty.

Statement c (Incorrect):

When expanding the expression two plus x, all cubed, the result should be eight plus twelve x plus six x squared plus x cubed. The statement incorrectly swaps the numbers in front of the x and x squared terms, making it incorrect.

Statement d (Incorrect):

Sitting three boys and three girls in a row means you are arranging a total of six people. The number of ways to arrange six people in a row is six factorial, which is equal to seven hundred twenty. The statement claims it is three hundred sixty, which is incorrect.