Home
Class 11
MATHS
Prove that : ^10P3= "^9P3+3^9P2....

Prove that :
`^10P_3= "^9P_3+3^9P_2`.

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    MODERN PUBLICATION|Exercise EXERCISE|319 Videos

  • MATHEMATICAL REASONING

    MODERN PUBLICATION|Exercise EXERCISE|169 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|348 Videos

Similar Questions

Explore conceptually related problems

Evaluate : "^10P_3 .

Find r if : "^10P_r= 2^9P_r .

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2) .

Prove that (9!)/((9 - 3)!) = 504

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : p_1^-2 + p_2^-2 + p_3^-2 = ((cot A+cot B+ cotC))/triangle .

If p_1, p_2, p_3 are the altitudes of a triangle from the vertices A, B, C and triangle , the area of the triangle, prove that : 1/p_1+1/p_2-1/p_3= (2ab)/((a+b+c)triangle) cos^2 frac (C)(2) .

Let P(n) be the statement " n^2-n+41 " is prime. Prove that P(1), P(2) and P(3) are true. Also prove that P(41) is not true. How does this not contradict the Principle of Induction ?

Find n if "^(n-1)P_3 : "^nP_4 =1:9 .

If P (n) is the statement : "2^(3n)- 1 is an integral multiple of 7”, prove that P(1), P(2) and P (3) are true.

MODERN PUBLICATION-PERMUTATIONS AND COMBINATIONS-EXERCISE
  1. Find n if "^(n-1)P3 : "^nP4 =1:9.

    Text Solution

    |

  2. Prove that : "^nPn= 2^nP(n-2).

    Text Solution

    |

  3. Prove that : ^10P3= "^9P3+3^9P2.

    Text Solution

    |

  4. Show that ^nPn= "^nP(n-1) for all natural numbers n .

    Text Solution

    |

  5. How many 3-digit numbers can be formed by using the digits 1 to 9 if n...

    Text Solution

    |

  6. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4,...

    Text Solution

    |

  7. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4...

    Text Solution

    |

  8. In how many ways can five children stand in a queue ?

    Text Solution

    |

  9. How many different signals can be generated from 6 flags of different ...

    Text Solution

    |

  10. Seven songs are to be rendered in a programme. In how many different o...

    Text Solution

    |

  11. There are 6 items in column A and 6 items in column B. A student is as...

    Text Solution

    |

  12. How many 3-digit numbers are there without repetition?

    Text Solution

    |

  13. How many 4-digit numbers are there with no digit repeated?

    Text Solution

    |

  14. How many natural numbers from 1 to 1000 have none of their digits repe...

    Text Solution

    |

  15. How many 3-digit even numbers can be made using the digits 1, 2, 3, 4,...

    Text Solution

    |

  16. How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4...

    Text Solution

    |

  17. Find the number of 4-digit numbersthat can be formed using the digits ...

    Text Solution

    |

  18. How many numbers lying between 100 and 1000 can be formed with the dig...

    Text Solution

    |

  19. How many 4 digits numbers can be formed from the digits 1 to 9 if not ...

    Text Solution

    |

  20. How many 4-digit numbers are there with no digit repeated?

    Text Solution

    |