3.21: 5-digit numbers and red/brown hair arrangements

0606/23/M/J/25 — Question 6 · 6 marks

(a)
Five of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to make a 5-digit number. Find how many ways this can be done when the 5-digit number is greater than 50 000.
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(b)(i)
In a group of 13 people, 7 have red hair and 6 have brown hair. The 13 people stand in line for a photograph. No person with red hair is standing next to another person with red hair. Find the number of different ways this can be done.
[2]
(b)(ii)
Chris chooses 5 people from this group. Find the number of ways Chris can do this if at least 1 person chosen has brown hair.
[2]