(i) A father brought his eight daughters on a bus for a trip. Assuming that all...

   

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(i) A father brought his eight daughters on a bus for a trip. Assuming that all seats are vacant when they entered the bus, how many ways can the father seats his daughters if four of them must sit in the front two rows of two seats on the right side and the remaining four in a row at the back of the bus with 5 seats (refer to the diagram below). Note: We shall disregard where the father sits. 4 daughters (ii) Driver 1000000 4 daughters How many ways can a club with 15 women and 9 men forms a committee of size six if the committee must have at least two men? [Hint: Explain your selections in terms of a task and subtasks.] (b) How many integers in the set {1,2,3,..., 400) are divisible by at least one of 4, 6, or 9? (Note: Simplify your working as much as possible and/or use set definitions.) (c) If repetition of digits is not allowed, how many three-digit numbers can be formed from 2, 3, 4, 5, 7 and 9 if: (i) (ii) there are no restrictions on the choices of digits? the numbers must be less than 500? (iv) the numbers must be multiples of 7? (iii) the numbers must be odd? (i) A father brought his eight daughters on a bus for a trip. Assuming that all seats are vacant when they entered the bus, how many ways can the father seats his daughters if four of them must sit in the front two rows of two seats on the right side and the remaining four in a row at the back of the bus with 5 seats (refer to the diagram below). Note: We shall disregard where the father sits. 4 daughters (ii) Driver 1000000 4 daughters How many ways can a club with 15 women and 9 men forms a committee of size six if the committee must have at least two men? [Hint: Explain your selections in terms of a task and subtasks.] (b) How many integers in the set {1,2,3,..., 400) are divisible by at least one of 4, 6, or 9? (Note: Simplify your working as much as possible and/or use set definitions.) (c) If repetition of digits is not allowed, how many three-digit numbers can be formed from 2, 3, 4, 5, 7 and 9 if: (i) (ii) there are no restrictions on the choices of digits? the numbers must be less than 500? (iv) the numbers must be multiples of 7? (iii) the numbers must be odd?