How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions ?

What is the maximum value of n such that 5ⁿ divides (30! + 35!), where n is a natural number?

What is the value of 2(2 × 1) + 3(3 × 2 × 1) + 4(4 × 3 × 2 × 1) + 5(5 × 4 × 3 × 2 × 1) + .................. + 9(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) + 2 ?

Consider the following statements:

1. $\frac{n!}{3!}$ is divisible by 6, where n > 3

2. $\frac{n!}{3!}+3 $ is divisible by 7, where n > 3

Which of the above statements is/are correct?