A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed ?
In an examination paper there are two sections each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any particular section. In how many ways can 5 questions be selected ?
There are 100 students in a college class of which 36 are boys studying statistics and 13 girls not studying statistics. If there are 55 girls in all, then the probability that a boy picked up at random is not studying statistics, is
There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Statistics and 9 are not studying statistics. The probability that a boy picked up at random is not studying Statistics = $9 \over 45$ = $1 \over 5$
Three boys and three girls are to be seated around a table in a circle. Among them the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible ?
There are seven letters in the word 'COUNTRY' and two vowels O and U. Considering two vowels as one unit, total number of letters will be 5 + 1 = 6. So, number of arrangements = 6! Now, the two vowels can be arranged in 2! ways among themselves. Total number of ways = 6! $\times$ 2! = 1440
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
There are six teachers. Out of them, two are primary teachers and two are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set. The number of ways in which they can do so, is
The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 $\times$ 6) = 720.
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 $\times$ 5 $\times$ 4) = 20.