PLEASE HELP WITH ALL QUESTIONS NEED HELP Thank you 1 2 3 Am

PLEASE HELP WITH ALL QUESTIONS. NEED HELP. Thank you !!!!

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Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, how many contain at least one queen (complement of \"no queens\")? Dealt from a standard deck, hands contain at least one queen

Solution

1)
Atleast one queen :
For no queens, we can do it as : 48C5, i.e 1712304
So, for atleast 1 queen, 2598960 - 1712304, i.e

886656 --> ANS

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2)
1 - P(1 tail) - P(0 tail)

1 - 6C1*(1/2)^1 * (1/2)^5 - (1/2)^6

0.890625 ---> ANS

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3)
14 members, 5 officers --> so 9 non-officers.

14C5 - n(no officer selected)

14C5 - 9C5

1876 --> ANS