A man has to plant exactly four varieties of flowers in a flower bed in his garden, one variety in each of the four rows, in an ascending order of height from the first row to the fourth row. The seven varieties available to the man, in ascending order of height, are red begonias (RB), pink petunias (PP), orange marigolds (OM), red geraniums (RG), white snapdragons (WS), yellow zinnias (YZ) and pink cosmos (PC). The following restrictions on color arrangements apply: No two varieties of the same color can be planted. Orange flowers cannot be planted in a row immediately adjacent to a row of yellow flowers. If the man does not plant any red flowers, then the total number of acceptable arrangements of the flower garden is

Explanation: If no red flowers are planted, the available varieties are {PP, OM, WS, YZ, PC}. We need 4 varieties in ascending height order, with no two same colors and no OM adjacent to YZ. No two same colors means we can use only one pink (PP or PC). Case 1: Use PP (and exclude PC). Available varieties in order: {PP, OM, WS, YZ}. Possible arrangements: (PP, OM, WS, YZ). Check OM not next to YZ: OM is next to WS, WS is next to YZ. OK. (PP, OM, WS, YZ) is 1 arrangement. Case 2: Use PC (and exclude PP). Available varieties in order: {OM, WS, YZ, PC}. Possible arrangements: (OM, WS, YZ, PC). Check OM not next to YZ: OM is next to WS, WS is next to YZ. OK. (OM, WS, YZ, PC) is 1 arrangement. Total acceptable arrangements: 2. (The source provides two arrangements as the answer).