The number of reset of ways of answering n ( ≥ 3) True and false type questions so that in a sequence of answers. Now match the items of column I with that of Column II.
Column-I | Column-II |
(i) If no two are consecutive, is/are | [A] 2 |
(ii) if at least three consecutive, is/Are | [B] nC3.2n–3 |
[C] nC3 2n–2 | |
[D] 2n–2 |
Text Solution
Verified by Experts(i) [A]; (ii) [C]
Ans.
(i) [A]
(ii) [C]
Sol. (i) If no two consecutive answers are to be the same, then they must alternate. This is possible in two ways HT HT HT ........TH TH TH ........
(ii) Three places out of n can be chosen in n C 3 ways.
These three places can be filled up in just two ways,
whereas the remaining n – 3 can be filled up in 2 n–3
ways. So total possible answers
= n C 3 . 2. 2 n–3 = n C 3 . 2 n–2
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