Modern Maths – Permutation & Combination

Q.1. City A is connected to 3 cities. Each of these 3 cities is connected to 5 different cities. All these 5 cities are connected to city B. What is the number of ways to reach city B from city
Q.2. What is the number of four-digit numbers that can be formed, with repetition, using the digits 1, 2, 3, 4, 5, 7 and 8?
Q.3. There is one direct road from A to B. There are two roads from A to D, three from D to C and three from C to B. If C and D are not on the direct road from A to B, in how many ways can Vishal travel from A to B? A person can travel in only direction on one road.
Q.4. How many words can be formed by arranging the letters of the word BLASTED such that B and E are never together?
Q.5. Seven lectures, three of which are on Economics, are to be scheduled one after the another, In how many ways can they be scheduled such that the Economics lectures are consecutive?
Q.6. There are 10 different fruits in a basket. In how many ways can the fruits be selected?
Q.7. In how many ways can three cards be selected from a pack of cards such that atleast one queen is selected?
Q.8. Amol’s mother has bought 2 boxes of chalks for him. One box has only white chalks and the other ha chalks of 5 different colours other than white. If Amol uses 3 chalks of different colours, how many different combinations are possible?
Q.9. If \[ {^n}C_x \] = 126 and \[ {^n}P_x \] = 3024, what are the respective values of n and x?
Q.10. Four medical representatives R1, R2, R3 and R4 are to visit one doctor each (D1, D2, D3 and D4) on Thrusday. R1 will not visit D1, and R2 will visit only D2 or D3. In how many ways can the visits be done such that no two representative visit the same doctor?
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