10. A coordinator at a local fundraiser has 14 volunteers to help out. There will be 3 volunteers working at the entrance door, 4 volunteers helping with the young children and 7 working at the tables with the fundraising activities.

a) In how many ways can the volunteers be assigned? [2]

b) Mary and Martha are new volunteers this year, so they should not be placed together. In how many ways can the volunteers be assigned so that Mary and Martha are not at the same station? [3]

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topeadeniran2 topeadeniran2 · Answer 1 · 2022-03-11T11:59:35+01:00

The combination and permutations computed shows that the number of ways that the volunteers can be assigned is 120120.

From the information given, the number of ways that the volunteers can be assigned will be:

= 14C3 × 11C4 × 7C7.

= (14 × 13 × 12)/6 × (11 × 10 × 9 × 8)/24

= 120120

Also, the number of ways that the volunteers can be assigned so that Mary and Martha are not at the same station will be:

= 12C1 × 11C4 × 7C7

= 12 × 330 × 1

= 3960

Learn more about permutations on:

https://brainly.com/question/1216161