Can someone show me to work these? 1) a student club consist of 10 girls and 8 g

Question

Can someone show me to work these? 1) a student club consist of 10 girls and 8 guys. A committee of 6 is to be selected. In how many ways can this be done if... A) the committee must have atleast 5 girls on it B) three officers(president, Vice President, secretary/ treasurer) are selected from ALL members Can someone show me to work these? 1) a student club consist of 10 girls and 8 guys. A committee of 6 is to be selected. In how many ways can this be done if... A) the committee must have atleast 5 girls on it B) three officers(president, Vice President, secretary/ treasurer) are selected from ALL members 1) a student club consist of 10 girls and 8 guys. A committee of 6 is to be selected. In how many ways can this be done if... A) the committee must have atleast 5 girls on it B) three officers(president, Vice President, secretary/ treasurer) are selected from ALL members

Explanation / Answer

A)

Since it has to has atleast 5 girls

so possible cases are

i) 5 girls and 1 guy

ii) 6 girls

i) number of ways =(selecting 5 girls from 10 girls and selecting 1 guy from 8 guys)

                            =10C5 * 8C1

                            =252 * 8

                            =2016

ii) number of ways = selecting 6 girls from 10 girls

                            =10C6

                            210

so total ways = 2016 +210

                            =2226

B)

Since 3 officers have to be selected for sure

so we have to select remaining (6-3) members from the remaining total (18-3) members

that means

we have to select remaining 3 members from the remaining total 15 members

This can be done in 15C3 ways =455 ways

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