Permutation/Combination: 4 letters are selected from the word SENDING. Find the number of words with...?

PART 1: 6! Ways to arrange 6 letters 6 x 5 x 4 x 3 x 2 x 1 720 ways PART 2: 1 choice for the first letter (E) and then 5! Ways to arrange the rest.

1 x 5 x 4 x 3 x 2 x 1 120 ways PART 3: 1 choice for the first letter (O) and 1 choice for the last letter (T) and then 4! Ways to arrange the rest. 1 x 4 x 3 x 2 x 1 x 1 24 ways PART 4: Think of the consonants as a unit.

So you have O, E, (VWLS) There are 3! Ways to arrange these units --> 3 x 2 x 1 = 6 ways Within each arrangement, you then have 4! To arrange the consonants within their group --> 4 x 3 x 2 x 1 = 24 ways 6 * 24 = 144 ways.

1) P(6, 6) = 6! You do not pay enough to do more than one exercise per submission.

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