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Maths A Level permutations and combinations questions

hey, i'm super stuck on the last two questions of a massive set of p&c questions and i would be forever grateful to anyone who could explain them to me please!!

Q1. 4 letters are picked at random from the word THURSDAY, what is the probability that there is at least one vowel among the letters? (answer:11/14)

Q2. how many numbers greater than 4000 can be formed by using some or all of the digits 8,6,5,3 and 2 without repetitions? (answer: 192)

thank youuu!!!
Q1. You work out the probability that no vowel is picked = (6/8) * (5/7) * (4/6) * (3/5) = (3/14). So then NOT(no vowel is picked) = 1 - (3/14) = 11/14


Q2. A Number over 4000 must begin with a number greater than or equal to 4 (in this case, that's only numbers 8, 6 and 5) or any 5 digit number. So the number of numbers over 4000 that can be made is 5 * 4 * 3 * 2 * 1 (5 digit numbers) + 3 * 4 * 3 * 2 (4 digit number beginning with 8, 6 or 5) = 192
Reply 2
Original post by BobBobson
Q1. You work out the probability that no vowel is picked = (6/8) * (5/7) * (4/6) * (3/5) = (3/14). So then NOT(no vowel is picked) = 1 - (3/14) = 11/14


Q2. A Number over 4000 must begin with a number greater than or equal to 4 (in this case, that's only numbers 8, 6 and 5) or any 5 digit number. So the number of numbers over 4000 that can be made is 5 * 4 * 3 * 2 * 1 (5 digit numbers) + 3 * 4 * 3 * 2 (4 digit number beginning with 8, 6 or 5) = 192


you legend thank you so much
Original post by romina23
you legend thank you so much


You're welcome

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