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大贈送_Secondary Easy Easy Maths!
1) How many even numbers less than 500 can be made from the integers 1,2,3,4,5, each integer being used once?Ans: 28 2) 4boxes each contain a large number of identical balls, those in one box are red, in second box are blue, in third box are yellow and those remaining are green. How many ways can five balls be... 顯示更多 1) How many even numbers less than 500 can be made from the integers 1,2,3,4,5, each integer being used once? Ans: 28 2) 4boxes each contain a large number of identical balls, those in one box are red, in second box are blue, in third box are yellow and those remaining are green. How many ways can five balls be chosen if: a) No restriction? ans:56 b)at least 1 is red? ans:35 3) How many different hands of 4 cards can be dealt from a pack of 52 playingcards if at least one of the cards is an "ace"? ans: 76145 4) In how many ways can 4 tins of fruit be chosen from a supermarket offering 10 varieties if at least 2 of the tins are of same variety? ans: 505 5) In how many ways can 3 letters from the word GREEN be arranged in a row if at least one of the letters is E? ans: 27 ******Please show all workings!!
最佳解答:
1) Simple counting helps. Starting from 1: we have 123, 124, 125, 132, 134, 135, 145. Starting from 2: we have 213, 214, 215, 231, 233, 234, 235, 245 Starting from 3: we have 312, 314, 315, 321, 324, 325, 345 Starting from 4: we have 412, 413, 415, 421, 423, 425, 435 We cannot start from 5 for the no. would be greater than 500 Total no. of req. integers = 7 x 4 = 28 =============================== 2) 5 balls from 4 colours => At least one colour must appear twice. (a) The pattern can be divided into 6 groups: [ 2-1-1-1 means one colour appears twice, other 3 each once. 3-2 means one colour appears 3 times, one two times, etc ] 2-1-1-1: No. = 1x4 = 4 2-2-1: No = 6x4/2 = 12 3-1-1: No. = 3x4 = 12 3-2: No. = 3x4 = 12 4-1: No. = 3x4 = 12 5: No. = 1x4 = 4 Total no. = 4x2 + 12x4 = 56 ====================== (b) No. = 56 - No. of ways without Red No. = 56 - 1/4 [No. of 2-2-1] - 1/4 [No. of 3-1-1] - 1/2 [No. of 3-2] - 1/2 [No. of 3-2] - 3/4 [No. of 5] No. = 56 - 3 - 3 - 6 - 6 - 3 = 35 ====================== 3) No, of ways = 52C4 - 48C4 No of ways = ( 52x51x50x49 - 48x47x46x45 ) / 4! No of ways = 76145 ================ 4) No. = 1/10 [ 10P6 ] + 1 = 505 ======================== 5) No. of ways = 5P3 - 3 (3 different letters, 3 different arrangements) No. of ways = 30 - 3 = 27 ==================== Hope I can help you.
其他解答:
1) How many even numbers 3x3x2 = 18
大贈送_Secondary Easy Easy Maths!
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發問:1) How many even numbers less than 500 can be made from the integers 1,2,3,4,5, each integer being used once?Ans: 28 2) 4boxes each contain a large number of identical balls, those in one box are red, in second box are blue, in third box are yellow and those remaining are green. How many ways can five balls be... 顯示更多 1) How many even numbers less than 500 can be made from the integers 1,2,3,4,5, each integer being used once? Ans: 28 2) 4boxes each contain a large number of identical balls, those in one box are red, in second box are blue, in third box are yellow and those remaining are green. How many ways can five balls be chosen if: a) No restriction? ans:56 b)at least 1 is red? ans:35 3) How many different hands of 4 cards can be dealt from a pack of 52 playingcards if at least one of the cards is an "ace"? ans: 76145 4) In how many ways can 4 tins of fruit be chosen from a supermarket offering 10 varieties if at least 2 of the tins are of same variety? ans: 505 5) In how many ways can 3 letters from the word GREEN be arranged in a row if at least one of the letters is E? ans: 27 ******Please show all workings!!
最佳解答:
1) Simple counting helps. Starting from 1: we have 123, 124, 125, 132, 134, 135, 145. Starting from 2: we have 213, 214, 215, 231, 233, 234, 235, 245 Starting from 3: we have 312, 314, 315, 321, 324, 325, 345 Starting from 4: we have 412, 413, 415, 421, 423, 425, 435 We cannot start from 5 for the no. would be greater than 500 Total no. of req. integers = 7 x 4 = 28 =============================== 2) 5 balls from 4 colours => At least one colour must appear twice. (a) The pattern can be divided into 6 groups: [ 2-1-1-1 means one colour appears twice, other 3 each once. 3-2 means one colour appears 3 times, one two times, etc ] 2-1-1-1: No. = 1x4 = 4 2-2-1: No = 6x4/2 = 12 3-1-1: No. = 3x4 = 12 3-2: No. = 3x4 = 12 4-1: No. = 3x4 = 12 5: No. = 1x4 = 4 Total no. = 4x2 + 12x4 = 56 ====================== (b) No. = 56 - No. of ways without Red No. = 56 - 1/4 [No. of 2-2-1] - 1/4 [No. of 3-1-1] - 1/2 [No. of 3-2] - 1/2 [No. of 3-2] - 3/4 [No. of 5] No. = 56 - 3 - 3 - 6 - 6 - 3 = 35 ====================== 3) No, of ways = 52C4 - 48C4 No of ways = ( 52x51x50x49 - 48x47x46x45 ) / 4! No of ways = 76145 ================ 4) No. = 1/10 [ 10P6 ] + 1 = 505 ======================== 5) No. of ways = 5P3 - 3 (3 different letters, 3 different arrangements) No. of ways = 30 - 3 = 27 ==================== Hope I can help you.
其他解答:
1) How many even numbers 3x3x2 = 18
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