No, sometimes they will be equal (when all items being permutated are all different, eg all permutations of {1, 2, 3} are distinguishable).
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No. The number of permutations or combinations of 0 objects out of n is always 1. The number of permutations or combinations of 1 object out of n is always n. Otherwise, yes.
Since there are no duplicate letters in the word RAINBOW, the number of permutations of those letters is simply the number of permutations of 7 things taken 7 at a time, i.e. 7 factorial, which is 5040.
If there are n different objects, the number of permutations is factorial n which is also written as n! and is equal to 1*2*3*...*(n-1)*n.
There are 16 choices for the first number and 15 choices for the second number (since repetition is not allowed). Thus, there are a total of 16 x 15 = 240 two-number permutations.
The word "numbers" consists of 7 distinct letters. The number of permutations of these letters is calculated using the factorial of the number of letters, which is 7!. Therefore, the total number of permutations is 7! = 5,040.