Counting - Day 4
Solutions - Day 4
1) 3 * 2 * 1 = 6 ways 3P3
2) 4 * 3 * 2 * 1 = 24 ways 4P4
3) 4 * 3 = 12 ways 4P2
4) 4 * 3 * 2 = 24 ways 4P3
5) 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 ways 7P7
6) 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880 9P9
7) 52 * 51 * 50 * 49 * 48 = 311,845,200 52P5
8) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE 5C3
9) 26 * 26 * 26 = 17,576 ways
10) 26 * 25 * 24 * 10 * 10 = 1,560,000
11) CART, CATR, CRAT, CRTA, CTAR, CTRA 4P4
ACRT, ACTR, ARCT, ARTC, ATCR, ATRC
RACT, RATC, RCAT, RCTA, RTAC, RTCA
TCAR, TCRA, TACR, TARC, TRCA, TRAC
CAR, CRA, CAT, CTA, CRT, CTR 4P3
ACR, ARC, ACT, ATC, ART, ATR
RAC, RCA, RAT, RTA, RCT, RTC
TAC, TCA, TAR, TRA, TRC, TCR
CA, CR, CT, AC, AR, AT, RA, RC, RT, TA, TC, TR 4P2
C, A, R, T 4P1 = 64 ways
12) 6 * 11 * 5 – 1 = 229 ways
Each selection has the option of not being selected. Therefore, when you have 5 appetizers to choose from you actually have the additional option of not choosing an appetizer, thus 6 choices. The same goes for each part of the meal. However, you have to eliminate the option of choosing nothing and nothing and nothing. That’s the reason for subtracting one.
1) 3 * 2 * 1 = 6 ways 3P3
2) 4 * 3 * 2 * 1 = 24 ways 4P4
3) 4 * 3 = 12 ways 4P2
4) 4 * 3 * 2 = 24 ways 4P3
5) 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 ways 7P7
6) 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880 9P9
7) 52 * 51 * 50 * 49 * 48 = 311,845,200 52P5
8) ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE 5C3
9) 26 * 26 * 26 = 17,576 ways
10) 26 * 25 * 24 * 10 * 10 = 1,560,000
11) CART, CATR, CRAT, CRTA, CTAR, CTRA 4P4
ACRT, ACTR, ARCT, ARTC, ATCR, ATRC
RACT, RATC, RCAT, RCTA, RTAC, RTCA
TCAR, TCRA, TACR, TARC, TRCA, TRAC
CAR, CRA, CAT, CTA, CRT, CTR 4P3
ACR, ARC, ACT, ATC, ART, ATR
RAC, RCA, RAT, RTA, RCT, RTC
TAC, TCA, TAR, TRA, TRC, TCR
CA, CR, CT, AC, AR, AT, RA, RC, RT, TA, TC, TR 4P2
C, A, R, T 4P1 = 64 ways
12) 6 * 11 * 5 – 1 = 229 ways
Each selection has the option of not being selected. Therefore, when you have 5 appetizers to choose from you actually have the additional option of not choosing an appetizer, thus 6 choices. The same goes for each part of the meal. However, you have to eliminate the option of choosing nothing and nothing and nothing. That’s the reason for subtracting one.