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### Mathematical Skills | Permutation and Computation

 Q. No. 1: The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR? A : 275 B : 251 C : 240 D : 242 Solution
 Q. No. 2: From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady? A : 246 B : 340 C : 290 D : 315 Solution
 Q. No. 3: In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated? A : 172000 B : 12600 C : 45920 D : 43200 Solution
 Q. No. 4: From 3 mangoes, 4 apples and 2 oranges, how many selections of fruits can be made, taking at least one of each kind? A : 327 B : 220 C : 315 D : 418 Solution
 Q. No. 5: Find the number of ways in which 21 books may be arranged on a shelf so that the oldest and the newest books never come together. A : 19! * 20! B : 19! * 21! C : 19 * 20! D : 2 * 19! Solution
 Q. No. 6: There 5 boys and 3 girls. In how many ways can they be seated in a row so that all the three girls do not sit together? A : 8! * 3! * 2! B : 6! * 50! C : 49 * 50! D : 50 * 6! Solution
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