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June 2016 p63 q6
2753
Three letters from the 9 letters of the word EVERGREEN are selected.
(iv) Find the number of selections which contain no Es and exactly 1 R.
(v) Find the number of selections which contain no Es.
Solution
(iv) The letters available without E are V, R, G, N. We need to select 3 letters with exactly 1 R. Possible selections are RVG, RVN, RGN. Thus, there are 3 ways.
(v) Without E, the letters are V, R, G, N. We need to select 3 letters:
No Rs: Only one way, VGN.
2 Rs: Choose 1 more letter from V, G, N. Possible selections are RRV, RRG, RRN, which is 3 ways.
\(Total selections without E: 1 (no Rs) + 3 (2 Rs) = 4 ways.\)