1. The product of r consecutive positive numbers in divisible by:
2. ${}^nC_r \times r!$=________?
3. The value of $4! \cdot 0! \cdot 1!$ is
4. If $r=n$, ${}^nC_r$ is equal to ________
5. Let $A=\{1,2,3,...,20\}$ Find the number of ways that the integer chosen is a prime number.
7. The number of ways in which $r$ letters can be posted in n-letter boxes in a town in;
8. 5 persons can be seated at a round table in how many ways?
9. Number of ways of arrangements of the word $\textbf{GARDEN}$
10. The value of $n$ if $^nC_{10} = \frac{12 \times 11}{2!}$:
11. The value of permutation $^{20}P_3$ is:
12. Factorial form $\frac{(n+1)(n)(n - 1)}{3 \cdot 2 \cdot 1}$ is
13. ${}^nC_r + {}^nC_{r-1}=?$
14. $\frac{^nP_r}{r!}$ is equal to:
15. factorial form of $n(n^2-1)=?$
16. From $A=\{1,3,5,7,9\}$ and $B=\{2,4,6,8\}$ if a Cartesian product $A \times B$ is chosen, then number of ways that $a+b=9$;
17. A student has to answer 10 out of 12 questions in an examination such that he must be choose at least 4 from first 5 questions. The nature of choice is:
18. $n$ different objects taken all at a time can be arranged in:
19. The factorial form of $\frac{10.9}{2.1}$ is
20. $(n - 1)(n - 2)(n - 3) \ldots (n - r + 1) = ?$
21. Factorial form of $n(n - 1)(n - 2) = ?$
22. Factorial notation was introduced by
23. If $n$ is a positive integer, then factorial of $n$ is denoted by ---
24. The total number of 6-digit numbers in which all the odd and only odd digit appear is
26. Number of words that can be formed from the letters of the word "PLANE'' using all letters at a time is equal to:
27. $^nP_r$ is equal to (where $n > 0$, $r > 0$):
28. If $^nC_5 = ^nC_4$, then $n$ is equal to:
29. If ${}^nC_4={}^nC_{10}$ then value of $n$ is;
30. If $^nC_r = ^nC_q$, which of the following must be true:
31. If $n$ is a negative integer then $n!$ is
32. If $r = n$, then $^nP_r$ equals:
33. ${}^nC_{r}={}^nC_{n-r}$ is useful when
34. Circular permutation of $n$ non-living things is given by:
35. If $3{}^nP_3={}^nP_4$ then value of n is:
36. $\frac{n!}{r!(n-r)!}$ is equal to:
37. Number of ways of arranging 5 keys in a circular ring is:
38. ${}^nC_{n-r}$ is equal to:
39. In how many ways a cricket team of 11 players out of 15 can be selected if the captain must be included in each way:
40. If ${}^{15}C_{3r}={}^{15}C_{r+3}$ then value of $r$ is:
41. The value of $n$ when $^{11}P_n = 11 \cdot 10 \cdot 9$ is:
42. ${}^nC_r$ is valid only if
43. The value of $\frac{4!}{0!}$ is
44. The number of permutations of the word "ANAMA" is:
45. The expression $\frac{(n - 1)!(n - 2)!}{(n!)^2}$ reduced to
