Help to solve question on Permutations and Combinations?

Ten lines are drawn parallel to the x-axis and nine lines parallel to the y-axis. Find the total number of rectangles (of all sizes) formed by these lines (excluding the axes).

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  • 7 years ago
    Favourite answer

    Ten lines are drawn parallel to the x-axis and nine lines parallel to the y-axis. Total number of rectangles (of all sizes) formed by these lines (excluding the axes) is given by

    N = Sigma(10 -- 1)*Sigma(9 -- 1) = (9*10/2)*(8*9/2) = 1620 ANSWER.

  • M3
    Lv 7
    7 years ago

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

    | x | x | x. | x | x | x. | x | x |

    ---------------- ----------------- x-axis

    from your description, i believe that any rectangles using either of the axes are not to be counted, so available lines are 9 parallel to the x-axis & 8 parallel to the y-axis

    # of rectangles 9c2 *8c2 = 36*28 = 1008 <-------

    if you say there are 10 & 9 parallel *apart* from the axes,

    then 10c2 *9c2 = 1620

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