Permutation (1 Viewer)

[ozidolroks]

" Words" are to be made from the letters REASON. How many 4-letter words are possible a) if the word contains both letters RN b) if R is included but 0 is excluded

can someone explain to me why the answers in a) is (4x3)4x3 and in
b) 4(4x3x2)

thanks

 

[gurmies]

For part a), you have REASON - 6 letters. R and N definitely have to be chosen and as there are only one each of them, there's only 1 R and 1 N to choose so 1 x 1. That leaves behind 4 letters, of which you need two -> so 4C2. Now you have your 4 letters selected, you must arrange them. 4!.4C2 = 144.

For part b), R definitely has to be chosen, and O cannot be chosen. This leaves 4 letters, of which you need to choose 3 -> so 4C3. You then have to arrange them, so 4!.4C3 = 96

Hope that's clear to you.