CAT Question of the Day Three men (Tom , Peter and Jack) and three women (Eliza , Anne and Karen) are spending a few months at a hillside. They are to stay in a row of nine houses, which are facing north, each one living in his or her own house. Following are the details given regarding each of their houses : - Anne , Tom and Jack don't want to stay in any house, which is at the end of the row
- Eliza and Anne needs the House on their neighbor to be empty
- When Karen, Peter and Jack stand facing north, Karen finds that houses of both Peter and Jack are on her left-hand side
- Between Anne and Jack's house there is just one vacant house
- The house occupied by Tom is next to the House at the end
- No two vacant houses are together, are no vacant house is at any end
- Let N be the total number of different arrangements of the houses in which they can stay
Denote n P(X) as the position of the house (from the left) at which the person X is staying and n P(X) ranges from 1 to 9 where n is the arrangement number (integer) and n =1 to N, so 2 P(Jack) will denote, the position of Jack's house from the left in the second arrangement, as there can be N different arrangements of houses n P(X) will take values accordingly, then which of the following is true? | OPTIONS | | |  | 1) | If 6 P(Jack) = 2 , 7 P(Peter) = 1, 7 P(Eliza) = 4 then 6 P(Anne) + 7 P(Karen) = 12 | | | 2) | If n P(Eliza) = 1,then number of possible values of n are 5 and if n P(Tom) = 1, then number of possible values of n is 1 | | | 3) | Value of N is 9 | | | 4) | Let Jack and Peter are neighbors in k different arrangements, let's number those arrangements as 1st, 2nd, . . . k-th arrangement, then
 | | | 5) | None of the above |
Tip of the Day The formula for calculating permutations is used when the order of the selected items matters while that of combinations is used when only the number of selected items matters, they may be selected in any random order. Last year's Question of the day (15-Apr-12) From among the options, choose the summary of the passage that is written in the same style as that of the passage
Imagine that you are French. You are walking along a busy pavement in Paris and another pedestrian is approaching from the opposite direction. A collision will occur unless you each move out of the other's way. Which way do you step? The answer is almost certainly to the right. Replay the same scene in many parts of Asia, however, and you would probably move to the left. It is not obvious why. There is no instruction to head in a specific direction. There is no simple correlation with the side of the road on which people drive: Londoners funnel to the right on pavements, for example. Instead, this is a behaviour brought about by probabilities. If two opposing people guess each other's intentions correctly, each moving to one side and allowing the other past, then they are likely to choose to move the same way the next time they need to avoid a collision. The probability of a successful manoeuvre increases as more and more people adopt a bias in one direction, until the tendency sticks. Whether it's right or left does not matter; what does is that it is the unspoken will of the majority.
| OPTIONS | | | | | 1) | Pedestrians in France would step to the right and Asians to the left to avoid collision with others depending on the side on which one is expected to drive. | | | 2) | The specific direction in which one turns in order to avoid collisions depends on the bias that people adopt based on the history of past successful manoeuvres. | | | 3) | Pedestrians' ability to avoid collision with each other by turning to the left or right is based on past successful manoeuvres forming a bias in more and more people of a society. | | | 4) | The reason for pedestrian avoiding collision with other pedestrians by stepping to the right or left is not obvious and may have to do with the side a society is expected to drive. |
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