Questions

1. Question 1

   Evaluate the following:

   (i)

   ${}^{10}P_5$

   (ii)

   ${}^5P_2$

   (iii)

   ${}^7P_7$

   (iv)

   ${}^{10}P_3$

   SolutionTheory
2. Question 2

   Find the value of $n$ when:

   (i)

   ${}^nP_3 = 504$

   (ii)

   ${}^{15}P_n = 15 \cdot 14 \cdot 13 \cdot 12 \cdot 11$

   (iii)

   ${}^nP_5 : {}^{n-2}P_2 = 540 : 1$

   SolutionTheory
3. Question 3

   Prove from the first principle that:

   (i)

   ${}^nP_r = n \cdot {}^{n-1}P_{r-1}$

   (ii)

   ${}^nP_r = {}^{n-1}P_r + r \cdot {}^{n-1}P_{r-1}$

   SolutionTheory
4. Question 4

   How many words can be formed from the letters of the following words using all letters when no letter is to be repeated:

   (i)

   PYTHON

   (ii)

   NETWORK

   (iii)

   COMPUTER

   SolutionTheory
5. Question 5

   How many signals can be given by 6 flags of different colours, using 2 flags at a time?

   SolutionTheory
6. Question 6

   How many signals can be given by 5 flags of different colours, when any number of flags are used at a time.

   SolutionTheory
7. Question 7

   How many 4 digit numbers can be formed, with distinct digits, with each digit odd?

   SolutionTheory
8. Question 8

   How many numbers between 100 and 1000 can be formed by using the digits 0, 1, 2, 3, 4, 5 without repetition? How many of them are divisible by 5?

   SolutionTheory
9. Question 9

   Find the numbers greater than 35000 that can be formed from the digits 1, 2, 3, 4, 5, 6, without repeating any digit.

   SolutionTheory
10. Question 10

    Find the number of 5-digit numbers that can be formed from the digits 1, 2, 4, 6, 8 (when no digit is repeated), but

    (i)

    the digits 2 and 8 are next to each other;

    (ii)

    the digits 2 and 8 are not next to each other.

    SolutionTheory
11. Question 11

    How many 6-digit numbers can be formed, without repeating any digit from the digits 0, 1, 2, 3, 4, 5? In how many of them will 0 be at the tens place?

    SolutionTheory
12. Question 12

    How many 5-digit multiples of 5 can be formed from the digits 2, 3, 5, 7, 9, when no digit is repeated.

    SolutionTheory
13. Question 13

    In how many ways can 8 different books including 2 on English be arranged on a shelf in such a way that the English books are never together?

    SolutionTheory
14. Question 14

    Find the number of arrangements of 3 different books on English and 5 different books on Urdu for placing them on a shelf such that the books on the same subject are together.

    SolutionTheory
15. Question 15

    In how many ways can 5 boys and 4 girls be seated on a bench so that the girls and the boys occupy alternate seats?

    SolutionTheory